1. 4.6 Quick Graphs Using Slope-Intercept Form 1 GOAL
Graphing Using Slope-Intercept Form
SLOPE-INTERCEPT FORM OF A LINEAR EQUATION
The equation of a line with slope m and y-intercept b is:
y = mx + b
EXAMPLE 1

2. Extra Example 1
Write the equation 3x + 4y = 8 in slope-intercept form. Then identify the slope and the y-intercept.
3x + 4y = 8
Solve for y:
y-intercept = 2
To graph a line using its slope and y-intercept, first plot the y-intercept, and then use the slope to graph at least one other point.
EXAMPLE 2

3. Extra Example 2 Graph 2x + y = 5. (0, 5)
First, write in slope-intercept form:
y = –2x + 5
Next, identify and plot the y-intercept:
b = 5
Now use the slope to
find another point and draw a line through the points:

4. In the coordinate plane, two vertical lines are parallel.
Two different lines in the same plane that do not intersect are _______.
parallel
In the coordinate plane, two vertical lines are parallel.
Two nonvertical lines are parallel if and only if they have the same ______.
slope
EXAMPLE 3

5. Since equations a and c have the same slopes, they are parallel.
Extra Example 3
Which of the following lines are parallel?
a. 3y = –9x – 5 b. 2y – 6x = –5 c. 12x + 4y = 1
Write each equation in slope-intercept form to determine their slopes:
a. b. c.
Since equations a and c have the same slopes, they are parallel.

6. Since each line has a slope of 2, they are parallel.
Checkpoint
Are the lines –2x + y = 5 and 4y = 8x – 1 parallel?
Since each line has a slope of 2, they are parallel.

7. 4.6 Quick Graphs Using Slope-Intercept Form 2 GOAL
SOLVING REAL-LIFE PROBLEMS
EXAMPLE 4

8. Extra Example 4
The equations below model the changing speeds of a car as it enters an expressway, travels on the expressway, and then exits the expressway. Create a graph to represent the car’s different speeds.
Stage 1 (first 2 minutes): s = 15t Domain: 0 ≤ t < 2
Stage 2 (next 10 minutes): s = 55 Domain: 2 ≤ t < 12
Stage 3 (next 2 minutes): s = –15t Domain: 12 ≤ t < 14

9. Extra Example 4 (cont.)
Stage 1 (first 2 minutes): s = 15t Domain: 0 ≤ t < 2
Stage 2 (next 10 minutes): s = 55 Domain: 2 ≤ t < 12
Stage 3 (next 2 minutes): s = –15t Domain: 12 ≤ t < 14
(2, 55)
(12, 55)
Speed (mi/h)
Time (min) 60 50 40 30 20 10
(14, 25)
(0, 25)

10. Checkpoint
Graph each line for the given domain on the same coordinate axes.
a. y = 2x Domain: –5 ≤ x < –3
b. y = 4 Domain: –3 ≤ x < –1
c. y = –4x Domain: –1 ≤ x < 0 y x