Presentation on theme: "4.6 Quick Graphs Using Slope-Intercept Form 1 GOAL"— Presentation transcript:
14.6 Quick Graphs Using Slope-Intercept Form 1 GOAL Graphing Using Slope-Intercept FormSLOPE-INTERCEPT FORM OF A LINEAR EQUATIONThe equation of a line with slope m and y-intercept b is:y = mx + bEXAMPLE 1
2Extra Example 1Write the equation 3x + 4y = 8 in slope-intercept form. Then identify the slope and the y-intercept.3x + 4y = 8Solve for y:y-intercept = 2To 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
3Extra Example 2 Graph 2x + y = 5. (0, 5) First, write in slope-intercept form:y = –2x + 5Next, identify and plot the y-intercept:b = 5Now use the slope tofind another point and draw a line through the points:
4In the coordinate plane, two vertical lines are parallel. Two different lines in the same plane that do not intersect are _______.parallelIn the coordinate plane, two vertical lines are parallel.Two nonvertical lines are parallel if and only if they have the same ______.slopeEXAMPLE 3
5Since equations a and c have the same slopes, they are parallel. Extra Example 3Which of the following lines are parallel?a. 3y = –9x – 5 b. 2y – 6x = –5 c. 12x + 4y = 1Write 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.
6Since each line has a slope of 2, they are parallel. CheckpointAre the lines –2x + y = 5 and 4y = 8x – 1 parallel?Since each line has a slope of 2, they are parallel.
74.6 Quick Graphs Using Slope-Intercept Form 2 GOAL SOLVING REAL-LIFE PROBLEMSEXAMPLE 4
8Extra Example 4The 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 < 2Stage 2 (next 10 minutes): s = 55 Domain: 2 ≤ t < 12Stage 3 (next 2 minutes): s = –15t Domain: 12 ≤ t < 14
9Extra Example 4 (cont.)Stage 1 (first 2 minutes): s = 15t Domain: 0 ≤ t < 2Stage 2 (next 10 minutes): s = 55 Domain: 2 ≤ t < 12Stage 3 (next 2 minutes): s = –15t Domain: 12 ≤ t < 14(2, 55)(12, 55)Speed (mi/h)Time (min)605040302010(14, 25)(0, 25)
10CheckpointGraph each line for the given domain on the same coordinate axes.a. y = 2x Domain: –5 ≤ x < –3b. y = 4 Domain: –3 ≤ x < –1c. y = –4x Domain: –1 ≤ x < 0yx