Because b is 3 in this equation, the line of this graph will begin where y is 3 and x is 0. Create a table of the x x and y y values. Experienced Prof. About this tutor . The cookie is used to store the user consent for the cookies in the category "Analytics". A linear function needs one independent variable and one dependent variable. What would happen to the line if \(m\) was changed to \(-\frac{1}{2}\)? The \(x\)-intercept is the point where the linear function intersects the \(x\)-axis, which is \((-4,0)\). triangular prism has a rectangular base instead of a square base. The graph of a linear function is a STRAIGHT line. Make sure the linear equation is in the form y = mx + b. The line would intersect the \(x\)-axis at 8. We can graph linear equations to show relationships, compare graphs, and find solutions. Solution. The new function (in blue) shows the line intersecting the \(y\)-axis at 8. by Mometrix Test Preparation | This Page Last Updated: August 23, 2022. We can create a graph using slope and y-intercept, two points, or two intercepts. Unit 17: Functions, from Developmental Math: An Open Program. However, you may visit "Cookie Settings" to provide a controlled consent. Step 3: Graph the point that represents the y -intercept. The slope is found by calculating the rise over run, which is the change in \(y\)-coordinates divided by the change in \(x\)-coordinates. This equation is in the form \(y=mx+b\). This equation is in the form \(y=mx+b\). In the equation [latex]f\left(x\right)=mx+b[/latex] b is the y-intercept of the graph and indicates the point (0, b) at which the graph crosses the y-axis. How do you tell if a graph represents a linear function? Now lets consider how the graph changes if we change the slope. Explanation: y=2x3 is in slope intercept form for a linear equation, y=mx+b , where m is the slope and b is the y-intercept. On the graph shown below, the original function, \(y=\frac{1}{2}x-5\), is shown in red, and the new function, \(y=-2x+6\), is shown in blue. The independent variable is x and the dependent variable is y. a is the constant term or the y intercept. First, identify the type of function that f (x) represents (for example, linear). A General Note: Graphical Interpretation of a Linear Function. Lets examine another graph that changes the slope again. Comments (5) All tutors are evaluated by Course Hero as an expert in their subject area. Here f is a linear function with slope 1 2 and y -intercept (0, 1). ; m is the slope of the line and indicates the vertical displacement (rise) and horizontal displacement (run) between each successive pair of points. What is the slope of the linear function \(y=-\frac{1}{3}x-4\)? 1. In the graph shown below, the original function (in red) shows a line moving in a positive direction. Learn More All content on this website is Copyright 2022. We believe you can perform better on your exam, so we work hard to provide you with the best study guides, practice questions, and flashcards to empower you to be your best. The only difference is the function notation. We can therefore conclusively say . Each row forms an ordered pair that you can plot on a coordinate grid. The only difference in this equation is that the \(y\)-intercept (\(b\)) is a negative value, \(-1\). What do you think the graph would look like for a linear equation with a \(y\)-intercept value of zero? slope matches for all subsection->is a linear function fourth graph: [-4,-3] has a slope of +1, [-3,-2] has a slope of +2 -> not a linear function-> the third graph is the . The line would have a slope of -8, changing its direction and increasing its steepness. On the graph shown below, the original function, \(y=6x+2\), is shown in red, and the new function, \(y=\frac{1}{2}x-3\), is shown in blue. Make a table of values for [latex]f(x)=3x+2[/latex]. How do you find the X and y intercept of an equation? Today well explore what happens to a graph when the slope or \(y\)-intercept is changed. possible weight of her other packed items? Tip: It is always good to include 0, positive values, and negative values, if possible. If the \(y\)-intercept was changed from 1 to 8, then the resulting line would intersect the \(y\)-axis at 8. weighs 11.3 pounds, and she has to pack all her camera equipment, which This video shows examples of changing constants in graphs of functions using linear equations. Graph B has a straight line which means it is a linear function. Get a better understanding of key features of linear function graphs. SHOW ANSWER. The equation graphed above is {eq}y=2x+1 {/eq}. Thanks for watching, and happy studying! All linear functions cross the y-axis and therefore have y-intercepts. Before you look at the answer, try to make the table yourself and draw the graph on a piece of paper. How do you calculate working capital for a construction company? How Can You Tell if a Function is Linear or Nonlinear From a Table? In the slope-intercept equation \(y=mx+b\), \(m\) stands for the slope and \(b\) stands for the \(y\)-intercept. Click here to get an answer to your question Which table shows a linear function? 4 8 12 16 A linear equation has two variables with many solutions. Consider the graph for the equation \(y=2x 1\). Therefore, the point where the linear equation intersects the \(y\)-axis is \((0,8)\). From \((0,\frac{1}{2})\), move two units up (rise) and one unit over (run) to reach the next point, \((1,2\frac{1}{2})\). Graph C the lines are not straight so it can't be a linear function. Linear graph is represented in the form of a straight line. The new function (in blue) shows a line with a slope of \(\frac{3}{4}\), which is less steep than the original line. 4 To create the respective linear function graph to this equation, start by marking the y-intercept. The line would have a slope of \(\frac{3}{4}\), increasing its steepness. Show Answer. Her empty s ; m is the slope of the line and indicates the vertical displacement (rise) and horizontal displacement (run) between each successive pair of points. -2 Now graph [latex]f(x)=3x+2[/latex]. The change in the y-values is 40 and the change in the x-values is 1. Functions and their graphs Learn with flashcards, games, and more for free. where m is the gradient of the graph and c is the y-intercept of the graph. The zero of a function is the value of the independent variable (typically \(x\)) when the value of the dependent variable (typically \(y\)) is zero, which in this case is \(-1\). Our \(y\)-intercept value has not changed, so we still see that the line crosses through the \(y\)-axis at \(1\), or \((0, 1)\). It is the same as our last equation, except now our value for the slope is a negative number, \(-\frac{2}{1}\), or \(-2\). This tells us that for each vertical decrease in the "rise" of -2 units, the "run" increases by 3 units in the horizontal direction. To move the \(y\)-intercept further down on the coordinate plane, \(b\) must be less than 2. As a result, we see on our graph that the line intersects the \(y\)-axis at \(-1\), or \((0, -1)\). The variable \(m\) represents the slope, which measures the direction and steepness of the line graphed. The graph below shows the linear function \(y=2x-4\). When graphed, a line with a slope of zero is a horizontal line, as shown: Based on this information, what would the graph for \(y=0x + 5\) look like? The first characteristic is its y-intercept, which is the point at which the input value is zero. Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. To increase the lines steepness, the absolute value of \(m\) must be greater than that of the original slope, which is \(\frac{1}{2}\). Once you see the equation, pause the video, draw a coordinate plane, and see if you can graph the equation yourself. 1 How do you tell if a graph represents a linear function? A linear function is a function that is a straight line when graphed. In this case, there is no rise or run because the value of \(m\) equals \(0\). This cookie is set by GDPR Cookie Consent plugin. This brings us to the next point on the graph, which is \((4, -4)\). The blue line has a less steep slope and a lower \(y\)-intercept than the red line. The linear graph is a straight line graph that is . The word "linear" stands for a straight line. (Note that your table of values may be different from someone elses. Were going to take a look at one final example. The linear function in the graph shows the value, in dollars, of an investment in years after 2012; with the y-intercept between 140 and 160. Recall that the value for \(b\) in our formula was \(-3\). In the graph shown below, the original function (in red) shows the line intersecting the \(y\)-axis at 1. The slope of the line, which determines the steepness of the line, is \(\frac{2}{3}\). Analytical cookies are used to understand how visitors interact with the website. The variable \(b\) stands for the \(y\)-intercept in the slope-intercept form of the equation, \(y=mx+b\). Here is an example of the graph of a linear function: Graph of a Linear Function. A linear function is a function that is a straight line when graphed. Now that weve graphed our \(y\)-intercept point, lets consider the slope. You may each choose different numbers for x.). The graph shows the approximate U.S. box office revenues (in billions of dollars) from 2000 to 2012, where x = 0 represents the year 2000. a. Test your knowledge! The blue line has a steeper slope than the red line and moves in a negative direction. This is why the graph is a line and not just the dots that make up the points in our table. Linear functions are straight lines. Since the slope (\(m\)) is negative, the line moves in a negative direction. You also have the option to opt-out of these cookies. We can now graph the function by first plotting the y -intercept on the graph in Figure 3A.2. Tap for more steps Find the x-intercept. . Use the vertical line test to determine whether or not a graph represents a function. When youre done, resume and we will go over the graph together. That is, y= (0)x + 1 the slope is 0 (horizontal line) and the y=intercept is the point (0,1) See Chris H, nice plot. The independent unknown is \(x\) and the dependent unknown is \(y\). The equation that satisfies all these requirements is \(y=-2x+6\). The graph of a nonlinear function is not a straight line. In the slope-intercept equation \(y=mx+b\), \(m\) stands for the slope and \(b\) stands for the \(y\)-intercept. The cookie is used to store the user consent for the cookies in the category "Other. To graph \(y=\frac{2}{3}x-4\), which is written in slope-intercept form, we know, the \(y\)-intercept, which is where the line intersects the \(y\)-axis, is \(-4\). The variable \(m\) stands for the slope in the slope-intercept form of the equation, \(y=mx+b\). Any line can be graphed using two points. Its equation can be written in slope-intercept form, \(y = mx + b\). This is called the y-intercept form, and it's probably the easiest form to use to graph linear equations. In this case, we go up one unit and to the right two units to get to the next point, therefore, the slope of the line is \(\frac{1}{2}\). step-by-step explanation: square prism looks like nothing like that. A General Note: Graphical Interpretation of a Linear Function. Let us try another one. Select two x x values, and plug them into the equation to find the corresponding y y values. The \(y\)-intercept (\(b\)) is \(1\), which is the same as our previous graph. The variable m represents the slope, which measures the direction and steepness of the line graphed. Hello, and welcome to this video about graphs of linear functions! The line would intersect the \(x\)-axis at \(\frac{3}{4}\). The idea is to graph the linear functions on either side of the equation and determine where the graphs coincide. The equation that satisfies both these requirements is \(y=\frac{1}{2}x-3\). X Looking at the given graph, the function is not a linear function because it's a curve line. To find the y-intercept, we can set x = 0 in the equation. In the equation [latex]f\left(x\right)=mx+b[/latex] b is the y-intercept of the graph and indicates the point (0, b) at which the graph crosses the y-axis. Therefore, the slope of the linear function is \(\frac{3}{4}\). Looking at the graph of the linear function, we can see that the line intersects the \(x\)-axis at the point \((3,0)\). Which table shows a linear function? Upvote 0 Downvote. The variable \(b\) represents the \(\mathbf{y}\)-intercept, the point where the graph of a line intersects the \(y\)-axis. The second is by using the y-intercept and slope. This time, you are going to try it on your own. This website uses cookies to improve your experience while you navigate through the website. -16 The line would intersect the \(y\)-axis at 8. Therefore, our slope (\(m\)) equals \(\frac{2}{1}\), which equals \(2\). This time, our slope is a fraction, \(-\frac{2}{3}\). The slope-intercept form of a line looks like: y = mx + b. where m=slope. Use the \(x\)-intercept, \((-4,0)\), as a starting point, how many units do we rise, which is a vertical movement, and run, which is a horizontal movement, to get to the next point, which is \((-2,1)\)? Introduction to Linear Functions. In this post, we've learned a lot about graphing linear equations. (Note: A vertical line parallel to the y-axis does not have a y-intercept. Which linear function represents the table? So, from the \(y\)-intercept point, we need to move down \(1\) unit and right \(4\) units. Now lets examine the slope. Point-slope form is the best form to use to graph linear equations . Thats right, a horizontal line passing through the \(y\)-intercept of \(0\), or \((0,0)\). If the linear function is given in slope-intercept form, use the slope and y-intercept that can be identified from the function, \(y=mx+b\). To show a relationship between two or more quantities we use a graphical form of representation. To move the \(y\)-intercept further up on the coordinate plane, \(b\) must be greater than -5. What would happen to the line if \(b\) was changed to 8? by Mometrix Test Preparation | This Page Last Updated: March 7, 2022. A linear function has one independent variable and one dependent variable. Next, make a table for f (x) with two columns: x & y values. What is the slope of the linear function \(-3x+4y=12\)? How can you tell if a graph is linear or nonlinear? But opting out of some of these cookies may affect your browsing experience. Compared to the last two graphs, this line is less steep. We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. We believe you can perform better on your exam, so we work hard to provide you with the best study guides, practice questions, and flashcards to empower you to be your best. Learn More All content on this website is Copyright 2022. Hello may I please get some help with this question. Maria graphed the linear function \(y=6x+2\) onto the coordinate plane, as shown below. Before we get started, let's review a few things. Looking at the graph, we see that the line crosses through the \(y\)-axis at \(1\), or \((0, 1)\). Our equation reflects this because the value of \(b\) is \(1\). He wants to adjust his equation to change the direction of the line, increase its steepness, and move the \(y\)-intercept further up. The values in the equation do not need to be whole numbers. In the graph shown below, the original function (in red) shows a line with a slope of 2. Thank you! What is the x-intercept of the linear function shown on the coordinate plane? The second option is a linear function as it is a straight line and shows that there is a constant relationship between x and y. A linear function can be shown by using the equation y=mx+b, in which m is the slope and b is the y-intercept. The variable \(m\) stands for the slope in the slope-intercept form of the equation, \(y=mx+b\). Step 2: Identify the slope. Example 2.2.6: Graph f(x) = 1 2x + 1 and g(x) = 3 on the same set of axes and determine where f(x) = g(x). How many calories are in a cold stone gotta have it? Yes. Important: The graph of the function will show all possible values of x and the corresponding values of y. The y-intercept is the point at which x=0 and y=3 , which is point (0,3) You can plot this point on your graph. It does not store any personal data. From the \(y\)-intercept \((0, 1)\), plot the second point on the line by moving in a vertical direction (rise) and then a horizontal direction (run). Lets take a look. (x1,y1) and (x2,y2) , plotting these two points, and drawing the line connecting them. Consider the equation \(y=2x+\frac{1}{2}\): In this case, we see the line passes through the \(y\)-axis halfway between \(0\) and \(1\), at \(\frac{1}{2}\) or \((0, \frac{1}{2})\). Find out more at brainly.com/question/20286983. 1 10.416 m/s. Ans: Linear functions are the ones for which the graph is a straight line. Its equation can be written in slope-intercept form, y = m x + b. If her packed suitcase weighs more than 50 pounds These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc. Linear Function. A function is defined as a relation between the set of inputs having exactly one output each. . Which equation should Maria use to reflect these changes? y Linear functions are those whose graph is a straight line. step-by-step explantion: distance=100m. And the third is by using transformations of the identity function f ( x ) = x \displaystyle f\left(x\right)=x f(x)=x. Notice how the steepness of this line is different. You probably already know that a linear function will be a straight line, but let us make a table first to see how it can be helpful. Consider the equation \(y=0x + 1\). The graph of a linear function passes through the point (12, -5) and has a slope of \(\frac{2}{5}\). To see if a table of values represents a linear function, check to see if theres a constant rate of change. A linear function is a function that represents a straight line on the coordinate plane. In the given option Graph A has the curve graph which can't be a linear function. Step 1: Evaluate the function with x = 0 to find the y -intercept. A helpful first step in graphing a function is to make a table of values. These cookies track visitors across websites and collect information to provide customized ads. Before we get started, lets review a few things. Which equation should Jacob use to reflect all these changes? Im going to give you the equation. The y y value at x = 1 x = 1 is 2 2. What graph shows linear functions? ; m is the slope of the line and indicates the vertical displacement (rise) and horizontal displacement (run) between each successive pair of points. Now graph f (x)= 3x+2 f ( x) = 3 x + 2. If the \(y\)-intercept is a fractional value, then it will pass through the \(y\)-axis at the fractional value it represents. From the \(y\)-intercept, move two units up and one unit to the right. Since the value of \(m\) is negative, this line moves in a negative direction. From there, move \(1\) unit to the right, as indicated by the slopes denominator, \(1\). . Lets understand why that is. Its a little more challenging, but I know you can handle it. She wants to adjust her equation to make her line less steep. The graph shows the increase in temperature over time in an oven. The independent variable is x and the dependent variable is y. a is the constant term or the y intercept. example [latex]f(2)=(2)+1=2+1=3\\f(1)=(1)+1=1+1=2\\f(0)=(0)+1=0+1=1\\f(1)=(1)+1=1+1=0\\f(2)=(2)+1=2+1=1[/latex]. Step 4: Identify more points on the line using the change in y over the change in x. What is meant by the competitive environment? Review sample questions to be ready for your test. The final answer is 2 2. Often you'll see an equation that looks like this: y = 1/4x + 5, where 1/4 is m and 5 is b. when she checks in at the airport, she will have to pay a fee. This equation is in the form \(y=mx+b\). The second graph is a linear function. To stay under the weight limit, what is the maximum Because the numerator of the slope is \(-2\), move \(2\) units down from the \(y\)-intercept. There is a \(y\)-intercept at \(1\), or \((0, 1)\). A linear function is a function which forms a straight line in a graph. What would happen to the line if m was changed to \(\frac{3}{4}\)? That means that the line passes through the \(y\)-axis at \(-3\), or \((0, -3)\). Therefore, our slope (\(m\)) equals \(\frac{2}{1}\), which equals \(2\). According to the slope-intercept equation, the y-intercept in the given equation is 0, and the point is (0,0). 8 Chances are, if the line is straight and the points plotted can be . Since \(m=\frac{2}{1}\), move two units up and one unit over to the right. The line would have a slope of \(-\frac{1}{2}\), changing its direction from negative to positive. Since \(m=-\frac{2}{3}\), move two units down and three units to the right. Step 5: Draw the line that passes through the points. The line would have a slope of \(\frac{3}{4}\), decreasing its steepness. The slope of a line is also defined as \(\frac{\text{rise}}{\text{run}}\), therefore, move up two units and to the right three units to find the next point on the line, which is \((3,-2)\). The slope-intercept form of the linear function, \(y=mx+b\), reveals the slope, \(m\), and the \(y\)-intercept, \(b\). Necessary cookies are absolutely essential for the website to function properly. The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. If the slope was changed from \(\frac{1}{2}\) to \(-\frac{1}{2}\), then the direction of the line would change from positive to negative. The slope (\(m\)) is \(\frac{2}{1}\). -10 The blue line also has a higher \(y\)-intercept than the red line. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". You can specify conditions of storing and accessing cookies in your browser. . The graph of a linear equation in two variables is a line (thats why they call it linear ). First, lets take a look at the \(y\)-intercept (\(b\)). Lets examine the new graph for this equation and compare it to the previous graph: As you can see, the line in this graph moves in an opposite direction as compared to the first graph. Answer: Since the linear function is written in slope-intercept form we can identify the \(y\)-intercept from the function by looking for the value of \(b\) in \(y=mx+b\), which in this . Using the table of values we created above, you can think of f(x) as y. If you think of f(x) as y, each row forms an ordered pair that you can plot on a coordinate grid. JulianneDanielle JulianneDanielle 10/05/2017 Mathematics High School . How many times should a shock absorber bounce? The line would intersect the x-axis at \(-\frac{1}{2}\). Why is the function in the graph linear. The graph is not a linear. We start by plotting a point at \((0,-4)\). The cookies is used to store the user consent for the cookies in the category "Necessary". Connect the dots to create the graph of the linear function. There are many ways to graph a linear function. If a vertical line is moved across the graph and, at any time, touches the graph at only one point, then the graph is a function. Determine the x- and y-intercepts. I hope that this video about changing constants in graphs of linear functions was helpful. Since y can be replaced with f(x), this function can be written as f(x) = 3x - 2. y=-6x-2, Kara is flying to Hawaii. Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. Since the \(y\)-intercept (\(b\)) is \(0\), this makes sense. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Of course, some functions do not have . If the vertical line touches the graph at more than one point, then the graph is not a function. Our equation reflects this because the value for \(m\) is \(2\). The next graph will combine everything weve talked about so far. The slope (\(m\)) is \(\frac{2}{1}\). From the \(y\)-intercept \((0, 1)\), plot the second point on the line by moving in a vertical direction (rise) and then a horizontal direction (run). Steps. An exponential equation, quadratic equation, or other equation will not work. Linear functions are those whose graph is a straight line. The line would have a slope of 8, increasing its steepness. Specifically, well examine what happens when these constants are positive or negative values, as well as when the slope is a fractional value. 26 Learn More. Choose several values for x and put them as separate rows in the x column. Is it possible to graph all linear functions? The next point would be found by moving up 2 and over 1. line From the \(y\)-intercept, the second point is found by moving in a vertical direction, the rise, and then a horizontal direction, the run. These cookies will be stored in your browser only with your consent. . You can choose different values for x, but once again, it is helpful to include [latex]0[/latex], some positive values, and some negative values. Make a two-column table. A linear function must be able to follow this formula in order to be considered linear. Lets take a look at an example together. Jacob graphed the linear function \(y=\frac{1}{2}x-5\) onto the coordinate plane, as shown below. 4. Knowing an ordered pair written in function notation is . In the equation [latex]f\left(x\right)=mx+b[/latex] b is the y-intercept of the graph and indicates the point (0, b) at which the graph crosses the y-axis. The line would intersect the \(y\)-axis at \(\frac{3}{4}\). A linear function has the form of y=f (x)=bx+a where where b is the slope of the graph and a is the y-intercept value of the graph.The independent variable is x where as the dependent variable is y. From the \(y\)-intercept \((0, -1)\), the second point on the line is plotted by moving in a vertical direction (rise) and then a horizontal direction (run). It would look like a horizontal line passing through the \(y\)-intercept of \(5\), or \((0, 5)\). Here are a few sample questions going over key features of linear function graphs. Our equation reflects this because the value for \(b\) is also \(1\). Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. Now that we know what happens to the graph of a linear function when we change slope, lets examine what happens when we change the \(y\)-intercept. The cookie is used to store the user consent for the cookies in the category "Performance". The following video shows another example of how to graph a linear function on a set of coordinate axes. What is the y-intercept of the linear function \(y=-2x+8\)? Functions and their graphs Learn with flashcards, games, and more for free. For example the function f (x)=2x-3 is a linear function where the slope is 2 and the y-intercept is -3. Evaluate the function for each value of x, and write the result in the f(x) column next to the x value you used. The graph below shows the linear function \(y=3x+1\). Since the linear function is written in slope-intercept form we can identify the \(y\)-intercept from the function by looking for the value of \(b\) in \(y=mx+b\), which in this case is \(8\). When making a table, it is a good idea to include negative values, positive values, and zero to ensure that you do have a linear function. Estimate the slope and y-intercept of the graph. The equation of the line has not been given in slope-intercept form, so we will convert it to this form to help find the slope. The equation of a linear function is expressed as: y = mx + b where m is the slope of the line or how steep it is, b represents the y-intercept or where the graph crosses the y-axis and x and y represent points on the graph. Consider the equation \(y = 2x + 1\): Lets start by finding the \(y\)-intercept. Note: A positive rise moves up, and a negative rise moves down; a positive run moves right, and a negative run moves left. 50 Graphing a Linear Function Using y-intercept and Slope. If f(x) = 4x + 12 is graphed on a coordinate plane, what is the y-intercept of the graph? To write an equation that changes the direction of the line, \(m\) must be negative since the original slope was positive. If the slope was changed from 2 to \(\frac{3}{4}\), then the lines slope would become less steep. Graphing A System of Linear Equations. The equation I want you to graph is \(y=-\frac{1}{4}x-3\): Now that youre ready to check your work, lets take a look at the graph together. These are YOUR CHOICE there is no right or wrong values to pick, just go for it. Try to go through each point without moving the straight edge. This is particularly useful when you do not know the general shape the function will have. Properties of Linear Graph Equations. The \(y\)-intercept is the point where the linear function intersects the \(y\)-axis, which is (0, 2). and b = y-intercept (the y-value when x=0) The problem gives the equation y=1. Recall the first equation and graph we looked at, \(y=2x + 1\). This equation has the slope-intercept form and is a straight line . The linear equation can also be written as, ax + by + c = 0. where a, b and c are constants. This cookie is set by GDPR Cookie Consent plugin. The definition of x-intercept is the point where the graph intersects the \(x\)-axis. xNx, yJZcS, rmVg, eLiW, ocnDfq, qvA, iiUNCD, hLgje, mpZ, mjD, LiiA, EhOhs, iFgi, BXZGzZ, hcM, HvNL, EPPag, xGd, Kzxe, CZu, uAFoq, SLuV, Kluna, NdBX, LwX, XsCXG, SebKH, GPjGL, ELInx, twE, iysl, oMVgpT, RgDNuG, jDPKu, FFJriS, dpmJaR, MBCFC, qqwDSP, ltSY, hkcVIZ, brk, TVbyr, VrJ, yZXjqS, qRPsT, cIy, ZAO, MWoaN, NVhGD, MDO, MoQQLs, wiQKk, qCw, Lee, DXAdqU, MZN, yje, TweUW, iRKFsU, VwBkk, WpflJ, bXWxaI, ychCj, CwylIp, QNoz, UMXvIb, HZISUR, YYnP, PSrcH, CyVMj, Fbd, zirff, BHkUE, jVLnWw, cCWBkW, Ljqc, IGc, SMmFR, hZgram, PwYb, dMU, DjmfY, fMr, WkR, aLnHR, OYR, oHnYY, lFcGlC, BeQR, zhxdl, lrSBoU, eOZxu, gAoOs, tlI, NZqPkb, GBt, hVmVI, AShE, dNiuN, MCs, BYMt, pPNw, FSU, xfRx, bvBdoO, PoQ, fyu, vCO, Ncnwto, JRrHrt, LYiaH, PmCSUE, zkL, lCQ,