1. § 1.3
Intercepts

2. Intercepts Example: Find the x-intercept of 4 = x – 3y Let y = 0.
Then 4 = x – 3y becomes
4 = x – 3(0) Replace y with 0.
4 = x Simplify the right side.
So the x-intercept is (4,0).

3. Intercepts Intercepts of axes (where graph crosses the axes)
Since all points on the x-axis have a y-coordinate of 0, to find the x-intercept, let y = 0 and solve for x.
Since all points on the y-axis have an x-coordinate of 0, to find the y-intercept, let x = 0 and solve for y.

4. Graph by Plotting Intercepts
Example:
Graph the linear equation 4 = x – 3y by plotting intercepts.
We previously found that the y-intercept is (0, ) and the x-intercept is (4, 0).
Along with the intercepts, for the third solution, let y = 1.
4 = x – 3(1) Replace y with 1.
4 = x – Simplify the right side.
4 + 3 = x Add 3 to both sides.
7 = x Simplify the left side.
So the third solution is (7, 1).
Continued.

5. Graph by Plotting Interceptsx y
Example continued:
Plot the two intercepts (0, ) and (4, 0) along with the third solution (7, 1).
(4, 0)
(7, 1)
(0, )
Draw the line that contains the three points.

6. Graph by Plotting Intercepts
Example:
Graph 2x = y by plotting intercepts
To find the y-intercept, let x = 0
2(0) = y
0 = y, so the y-intercept is (0,0)
To find the x-intercept, let y = 0
2x = 0
x = 0, so the x-intercept is (0,0)
Notice that the x- and y-intercept are the same point.
Continued.

7. Graph by Plotting Intercepts
Example continued:
Find two other solutions to the equation.
Let x = 3
2(3) = y
6 = y, so another point is (3, 6)
Let y = 4
2x = 4
x = 2, so another point is (2, 4)
Continued.

8. Graph by Plotting Interceptsx y
Example continued:
(3, 6)
(0, 0)
(2, 4)
Plot all three of the solutions (0, 0), (3, 6) and (2, 4).
Draw the line that contains the three points.

9. Vertical and Horizontal Lines
Vertical Lines
The graph of x = c, where c is a real number is a vertical line with x-intercept (c, 0).
Horizontal Lines
The graph of y = c, where c is a real number, is a horizontal line with y-intercept (0, c).

10. Graph by Plotting Intercepts
Example:
Graph y = 3
Note that this line can be written as y = 0·x + 3
The y-intercept is (0, 3), but there is no x-intercept.
(Since an x-intercept would be found by letting y = 0, and 0  0·x + 3, there is no x-intercept.)
Every value we substitute for x gives a y-coordinate of 3.
The graph will be a horizontal line through the point (0,3) on the y-axis.
Continued.

11. Graph by Plotting Interceptsx y
(0, 3)
Example continued:
y = 3

12. Graph by Plotting Intercepts
Example:
Graph x = – 3.
This equation can be written x = 0·y – 3.
When y = 0, x = – 3, so the x-intercept is (– 3,0), but there is no y-intercept.
Any value we substitute for y gives an x-coordinate of –3.
So the graph will be a vertical line through the point (– 3,0) on the x-axis.
Continued.

13. Graph by Plotting Interceptsx y
(– 3, 0)
Example continued:
x = – 3