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Slope Problems

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**(x1,y1) (x2,y2) Slope Problem Examples**

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

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**(0,-3) (1,-1) (-1,5) 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. +1 +2 To find another point on the line, repeat this process with your new point -1 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) (0,-3) +1 +2 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. (1,-1) (-1,5)

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**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 -3x +4 Now plot the y intercept -4 -4 Change in y Change in x y intercept slope From the y intercept, count the slope 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 What is the common thing you notice about the x-intercepts of these lines? (-1,0) (2,0) (6,0) 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 (0,5) (0,4) What is the common thing you notice about the y-intercepts of these lines? (0,1) 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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**Find the x-intercept. Let's look at the equation 2x – 3y = 12**

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

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**Find the y-intercept. 2x – 3y = 12**

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

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1.4 Linear Equations in Two Variables

1.4 Linear Equations in Two Variables

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