|
|
Chapter 12 Graphing 12-6 Finding Intercepts Definition An intercept is point where a line crosses one of the coordinate axes. - The y-intercept of a line is the point where the line crosses the y axis.
- The x-intercept of a line is the point where the line crosses the x axis.
| - The y-intercept always occurs at the point where x = 0. So when you need to determine the y-intercept of a line, find the value of y when x = 0.
- The x -intercept always occurs at the point where y = 0. So when you need to determine the x-intercept of a line, find the value of x when y = 0.
Procedure - Given the equation of a line, you can find the y-intercept by
- Set x = 0
- Solve for y
- Given the equation of a line, you can find the x-intercept by setting y = 0 and solving for x.
- Set y = 0
- Solve for x
| Example Determine the y-intercept of the line, 4x + 2y = 5. | The Problem | | Determine the y-intercept of the line, 4x + 2y = 5. | Step 1: Set x = 0 | 4(0) + 2y = 5
2y = 5 | | Step 2: Solve for y | y = 5/2 = 2.5 | | | The Solution | | The y-intercept of 4x + 2y = 5 is 2.5 | If you plot this line on a coordinate plane, you will see that it crosses the y axis at (0,2.5). Example Determine the x-intercept of the line, 4x + 2y = 5. | The Problem | | Determine the x-intercept of the line, 4x + 2y = 5. | Step 1: Set y = 0 | 4x + 2(0) = 5
4x = 5 | | Step 2: Solve for x | x = 5/4 = 1.25 | | | The Solution | | The x-intercept of 4x + 2y = 5 is 1.25 | If you plot this line on a coordinate plane, you will see that it crosses the x axis at (0,1.25).
|
