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

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

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:

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

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.

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.

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

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 + 25 Domain: 0 ≤ t < 2 Stage 2 (next 10 minutes): s = 55 Domain: 2 ≤ t < 12 Stage 3 (next 2 minutes): s = –15t + 235 Domain: 12 ≤ t < 14

Extra Example 4 (cont.) Stage 1 (first 2 minutes): s = 15t + 25 Domain: 0 ≤ t < 2 Stage 2 (next 10 minutes): s = 55 Domain: 2 ≤ t < 12 Stage 3 (next 2 minutes): s = –15t + 235 Domain: 12 ≤ t < 14 (2, 55) (12, 55) Speed (mi/h) Time (min) 0 2 4 6 8 10 12 14 60 50 40 30 20 10 (14, 25) (0, 25)

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