Finding intercepts of Linear Equations:

An x-intercept is the x-coordinate of a point where a graph crosses the x-axis. The x-intercept has a y value of zero.

A y-intercept is the y-coordinate of a point where a graph crosses the y-axis. The y-intercept has an x value of zero.

Example:

Find the x-intercept and y-intercept for the graph of the line.

Solution:

The x-intercept of this graph is 4. The coordinates of the point at the x-intercept is (4, 0).

The y-intercept of this graph is 2. The coordinates of the point at the y-intercept is (0, 2).

Finding the x-intercept:

Example:

Find the x-intercept of the graph of the equation 2x - 3y = 8.

Solution:

To find the x-intercept of 2x - 3y = 8, let y = 0.

2x - 3y = 8

2x - 3(0) = 8

2x = 8

x = 4 The x-intercept is 4. The line crosses the x-axis at the point (4, 0).

 

Finding the y-intercept:

Example:

Find the y-intercept of the graph of the equation 3x + 2y = -6.

Solution:

To find the y-intercept of 3x + 2y = -6, let x = 0.

3x + 2y = -6

3(0) + 2y = -6

2y = -6

y = -3 The y-intercept is -3. The line crosses the y-axis at the point (0, -3).

Assignment:

Find the x-intercept of the graph of each equation.

1. -x + 3y = -18

2. 2x - 2y = 10

3. -2x - y = 6

4. -3x + 4y = 12

5. 3x + 3y = -10

Find the y-intercept of the graph of each equation.

6. -2x -3y = 35

7. 3x + 5y = -10

8. 4x - 3y = 21

9. 0.5x + 0.4y = 16

10. -3x - 2y = 4

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