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Slope Problems

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Slope Problem Examples Determine a value for x such that the line through the points has the given slope. Let's use the slope formula and plug in what we know. (x1,y1)(x1,y1)(x2,y2)(x2,y2) You can cross-multiply to find a fraction-free equation for x to solve.

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Example when you have a point and the slope A point on a line and the slope of the line are given. Find two additional points on the line. 0 Remember that slope is the change in y over the change in x. The slope is 2 which can be made into the fraction (0,-3) So this point is on the line also. You can see that this point is changing (adding) 2 to the y value of the given point and changing (adding) 1 to the x value To find another point on the line, repeat this process with your new point (0,-3) +1+2 (1,-1) (-1,5)

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y intercept slope Example of given an equation, find the slope and y intercept Find the slope and y intercept of the given equation and graph it. First let's get this in slope- intercept form by solving for y. -3x Now plot the y intercept From the y intercept, count the slope Change in y Change in x Now that you have 2 points you can draw the line

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Example of how to find x and y intercepts to graph a line The x-intercept is where a line crosses the x axis (6,0) (-1,0) (2,0) What is the common thing you notice about the x-intercepts of these lines? The y value of the point where they cross the axis will always be 0 To find the x-intercept when we have an equation then, we will want the y value to be zero.

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Now let's see how to find the y-intercept The y-intercept is where a line crosses the y axis (0,4) (0,1) (0,5) What is the common thing you notice about the y-intercepts of these lines? The x value of the point where they cross the axis will always be 0 To find the y-intercept when we have an equation then, we will want the x value to be zero.

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Let's look at the equation 2x – 3y = 12 Find the x-intercept. We'll do this by plugging 0 in for y 2x – 3(0) = 12 Now solve for x. 2x = x = 6 So the place where this line crosses the x axis is (6, 0)

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2x – 3y = 12 Find the y-intercept. We'll do this by plugging 0 in for x 2(0) – 3y = 12 Now solve for y. -3y = y = - 4 So the place where this line crosses the y axis is (0, -4) We now have enough information to graph the line by joining up these points (6,0) (0,- 4)

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