# Slope and Intercept

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```					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
3
2                       2
2
1                       1
1
x                       x
x           1   2   3               1   2   3
1       2   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 y-
intercept 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                                                     3 
x                           So the x-intercept is  ,0  or (1.5, 0)
2                                                     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.

```
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