Study Guide: Section 6-4

Writing Linear Equations in Slope-Intercept Form

The x-coordinate of the point where a line crosses the x-axis is called the x-intercept. Similarly, the y-coordinate of the point where the line crosses the y-axis is called the y-intercept.

Definition of Intercepts

If an equation is given in standard form Ax + By = C and B ≠ 0, then:

the slope of the line (if B ≠ 0) is −A
B
the y-intercept of the line (if B ≠ 0) is C
B
the x-intercept of the line (if A ≠ 0) is C
A

Example 1

Find the x- and y-intercepts of the graph 5x − 2y = 10. Then write the equation in slope-intercept form.

Example 1 Intercepts Calculation

Thus, the x-intercept is 2, and the y-intercept is −5. The equation of the line in slope-intercept form is y = 5/2x − 5.

Example 2

Find the equation of a line given that it has a slope of 3 and passes through the point (−6, 4).

y = mx + b
4 = 3(−6) + b
4 = −18 + b
b = 22

Thus the equation of the line in slope-intercept form will be y = 3x + 22.

Practice Problems

Directions: Find the x- and y-intercepts of the graph of each equation.

1. 5x + 4y = 20

4, 5

2. 2x − 5y = −7

−7/2, 7/5

3. 4x − 8y = 10

5/2, −5/4

4. 9x + y = −1

−1/9, −1

Directions: Write an equation in slope-intercept form of a line with the given slope and y-intercept. Then write the equation in standard form.

5. m = 6, b = 10

y = 6x + 10,  6x − y = −10

6. m = 4, b = 0

y = 4x,  4x − y = 0

7. m = −1, b = 3

y = −x + 3,  x + y = 3

8. m = 2, b = −3

y = 2x − 3,  2x − y = 3

Directions: Find the slope and y-intercept of the graph of each equation. Then write each equation in slope-intercept form.

9. 0.2x + 0.5y = 1.6

−2/5, 16/5;  y = −2/5x + 16/5

10. 3x + 7y = 10

−3/7, 10/7;  y = −3/7x + 10/7

11. 6x − y = 9

6, −9;  y = 6x − 9

12. 14x − 21y = 7

2/3, −1/3;  y = 2/3x − 1/3