Math 72
Slope and Intercept
Names:
Friday, we learned how to find the slope between two points. We also discovered that a
linear equation (or line) has the same slope everywhere. Below, you see graphs of lines.
1. For each of the graphs, label 2 points on the line and find the slope between those
two points.
y
y
y
3
3
2
2
3
2
1
1
1
x
1
2
x
1
2
3
x
1
2
3
3
Now we are going to look at a few other characteristics of graphs. The point where the
graph crosses the x-axis is called the x-intercept. I have labeled the x-intercept and yintercept on the graph below.
y
y = 2x - 3
3
2
1
(1.5, 0) x-intercept
x
1
2
3
(0, -3)
y-intercept
2. Label the x-intercept and y-intercept on the three graphs in number 1 above. Be
sure to give both coordinates of the points.
3. What do you notice about the y-coordinates in each of the x-intercepts?
4. What do you notice about the x-coordinates of the y-intercepts?
The example graph on the previous page has been labeled with the equation y = 2x-3.
We can find the x-intercept and y-intercept by simply working with this equation. To
find the x-intercept, we set y equal to zero and solve for x.
Example: Set y = 0
0 = 2x – 3
3 = 2x
3
x
2
3 
So the x-intercept is  ,0  or (1.5, 0)
2 
Similarly, we can find the y-intercept by setting x = 0 and solving for y.
Example: Set x = 0
y = 2(0) –3
y=0–3
y = -3
So the y-intercept is (0, -3)
5. Using the above method, find the x- and y-intercepts of each of the following
equations.
1
a. y = -5x + 35
b. y = x  6
c. y = -13x
4
6. Make graphs of the equations in number 5 on separate axes. To make each graph,
plot the x-intercept and y-intercept and connect them with a line.