1. Slope Problems

2. (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.

3. (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)

4. 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

5. 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.

6. 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.

7. 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

8. 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)