1. Using Slopes and Intercepts
Course 3
12-3
Using Slopes and Intercepts
Warm Up
Find the slope of the line that passes through each pair of points
(3, 6) and (–1, 4)
2. (1, 2) and (6, 1) –

2. Using Slopes and Intercepts
Course 3
12-3
Using Slopes and Intercepts
Learn to use slopes and intercepts to graph linear equations.

3. Insert Lesson Title Here
Course 3
12-3
Using Slopes and Intercepts
Insert Lesson Title Here
Vocabulary
x-intercept
y-intercept
slope-intercept form

4. Using Slopes and Intercepts
Course 3
12-3
Using Slopes and Intercepts
You can graph a linear equation easily by finding the x-intercept and the
y-intercept. The x-intercept of a line is the value of x where the line crosses the x-axis (where y = 0). The y-intercept of a line is the value of y where the line crosses the y-axis (where x = 0).

5. Using Slopes and Intercepts
Course 3
12-3
Using Slopes and Intercepts
Additional Example 1: Finding x-intercepts and
y-intercepts to Graph Linear Equations
Find the x-intercept and y-intercept of the line 4x – 3y = 12. Use the intercepts to graph the equation.
Find the x-intercept (y = 0).
4x – 3y = 12
4x – 3(0) = 12
4x = 12 4x 4 12 =
x = 3
The x-intercept is 3.

6. Additional Example 1 Continued
Course 3
12-3
Using Slopes and Intercepts
Additional Example 1 Continued
Find the y-intercept (x = 0).
4x – 3y = 12
4(0) – 3y = 12
–3y = 12
–3y –3 12 =
y = –4
The y-intercept is –4.

7. Additional Example 1 Continued
Course 3
12-3
Using Slopes and Intercepts
Additional Example 1 Continued
The graph of 4x – 3y = 12 is the line that crosses the x-axis at the point (3, 0) and the y-axis at the point (0, –4).

8. Using Slopes and Intercepts
Course 3
12-3
Using Slopes and Intercepts
The form Ax + By = C, where
A, B, C are real numbers, is called the Standard Form of a Linear Equation.
Helpful Hint

9. y = mx + b Using Slopes and Intercepts 12-3
Course 3
12-3
Using Slopes and Intercepts
In an equation written in slope-intercept form, y = mx + b, m is the slope and b is the y-intercept.
y = mx + b
Slope
y-intercept

10. Using Slopes and Intercepts
Course 3
12-3
Using Slopes and Intercepts
Additional Example 2A: Using Slope-Intercept Form to Find Slopes and y-intercepts
Write each equation in slope-intercept form, and then find the slope and y-intercept.
2x + y = 3
2x + y = 3
–2x –2x
Subtract 2x from both sides.
y = 3 – 2x
Rewrite to match slope-intercept form.
y = –2x + 3
The equation is in slope-intercept form.
m = –2
b = 3
The slope of the line 2x + y = 3 is –2, and the y-intercept is 3.

11. Additional Example 4: Writing Slope-Intercept Form
Course 3
12-3
Using Slopes and Intercepts
Additional Example 4: Writing Slope-Intercept Form
Write the equation of the line that passes through (3, –4) and (–1, 4) in slope-intercept form.
Find the slope. =
y2 – y1
x2 – x1
4 – (–4)
–1 – 3 8 –4 =
= –2
The slope is –2.
Substitute either point and the slope into the slope-intercept form.
y = mx + b
Substitute –1 for x, 4 for y, and –2 for m.
4 = –2(–1) + b
4 = 2 + b
Simplify.

12. Additional Example 4 Continued
Course 3
12-3
Using Slopes and Intercepts
Additional Example 4 Continued
Solve for b.
4 = 2 + b
–2 –2
Subtract 2 from both sides.
2 = b
Write the equation of the line, using –2 for m and 2 for b.
y = –2x + 2

13. Using Slopes and Intercepts Insert Lesson Title Here
Course 3
12-3
Using Slopes and Intercepts
Insert Lesson Title Here
Lesson Quiz
Write each equation in slope-intercept form, and then find the slope and y-intercept.
1. 2y – 6x = –10
Write the equation of the line that passes through each pair of points in slope-intercept form.
3. (0, 2) and (4, –1)
y = 3x – 5; m = 3; b = –5
y = – x + 2 3 4