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LESSON 2.4 TEKS a.5, a.6 P ROBLEM M ETHOD P RACTICE Using Another Way to Solve Example 4, page 100 MULTIPLE REPRESENTATIONS In Example 4 on page 100, you wrote an equation of a line through two given points by first writing the equation in point-slope form and then rewriting it in slope-intercept form. You can also write an equation of a line through two points by using the slope-intercept form to solve for the y-intercept. Write an equation of the line that passes through (5, 22) and (2, 10). Solving for the y-Intercept To write an equation of a line through two points, you can substitute the slope and the coordinates of one of the points into y 5 mx 1 b and solve for the y-intercept b. STEP 1 Find the slope of the line. STEP 2 Substitute the slope and the coordinates of one point into the slope-intercept form. Use the point (5, 22). STEP 3 Solve for b. STEP 4 Substitute m and b into the slope-intercept form. 1. WRITE AN EQUATION Use the method above to write an equation of the line that passes through (2, 15) and (7, 35). 2. FITNESS At a speed of 45 yards per minute, a 120 pound swimmer burns 420 calories per hour and a 172 pound swimmer burns 600 calories per hour. Use two different methods to write a linear equation that models the number of calories burned per hour as a function of a swimmer’s weight. 3. SAFETY A motorist lights an emergency flare after having a flat tire. After burning for 6 minutes, the flare is 13 inches long. After burning for 20 minutes, it is 6 inches long. Use two different methods to write a linear equation that models the flare’s length as a function of time. ALTERNATIVE METHODS m 5 10 2 (22) } 2 2 5 y 5 mx 1 b 22 5 24(5) 1 b 22 5220 1 b 18 5 b y524x 1 18 5 12 } 23 5 24 4. SNOWFALL After 4 hours of snowfall, the snow depth is 8 inches. After 6 hours of snowfall, the snow depth is 9.5 inches. Use two different methods to write a linear equation that models the snow depth as a function of time. 5. ARCHAEOLOGY Ancient cities often rose in elevation through time as citizens built on top of accumulating rubble and debris. An archaeologist at a site dates artifacts from a depth of 54 feet as 3500 years old and artifacts from a depth of 26 feet as 2600 years old. Use two different methods to write a linear equation that models an artifact’s age as a function of depth. 6. REASONING Suppose a line has slope m and passes through (x 1 , y 1 ). Write an expression for the y-intercept b in terms of m, x 1 , and y 1 . Using Alternative Methods 105
MIXED REVIEW FOR TEKS TAKS PRACTICE Lessons 2.1–2.4 MULTIPLE CHOICE 1. WEBSITES From January through June, the number of visitors to a news website increased by about 1200 per month. In January, there were 50,000 visitors to the website. Which equation shows the number of visitors v as a function of the number of months t since January? TEKS a.3 A v 5 50,000 2 1200t B v 5 50,000 1 1200t C v 5 1200 2 50,000t D v 5 1200 1 50,000t 2. SLOPE What is the slope of a line parallel to the line 1 } y 2 3x 5 5? TEKS a.5 4 F 23 G 2 3 } 4 H 1 } 4 J 12 3. PARALLEL LINES Which equation represents a line that is parallel to the line x 1 3y 5 12 and contains no points in Quadrant I? TEKS a.5 A y 52 1 } 3 x 2 4 B y 52 1 } 3 x 1 8 C y 523x 2 4 D y 5 3x 1 4 4. POPULATION The official population of Baton Rouge, Louisiana, was 219,478 in 1990 and 227,818 in 2000. What is the average rate of change in the population from 1990 to 2000? TEKS a.5 F 28340 people per year G 2834 people per year H 834 people per year J 8340 people per year 106 Chapter 2 Linear Equations and Functions classzone.com 5. FOOTBALL The costs of general admission and student tickets to a high school football game are shown below. Ticket sales for one game totaled $11,200. Which equation gives the possible numbers of general admission tickets g and student tickets s that were sold? TEKS a.3 A 11,200 5 4g 2 7s B 11,200 5 4g 1 7s C 11,200 5 7g 2 4s D 11,200 5 7g 1 4s 6. PHOTOGRAPHY Your digital camera has a 512 megabyte memory card. You take pictures at two resolutions, a low resolution requiring 4 megabytes of memory per image and a high resolution requiring 8 megabytes of memory per image. Which equation gives the possible numbers of high resolution photos x and low resolution photos y you can take? TEKS a.3 F 8x 1 4y 5 512 G 4x 1 8y 5 512 H 8x 2 4y 5 512 J 4x 2 8y 5 512 GRIDDED ANSWER 0 1 2 3 4 5 6 7 8 9 7. SLOPE What is the slope of a line perpendicular to the line shown? Round your answer to the nearest hundredth. TEKS a.5 (0, 3) 1 y 1 (5, 0) x
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REVIEW SYSTEMS For help with solvin
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