VIEWS: 4 PAGES: 3 POSTED ON: 9/16/2012 Public Domain
Lesson 4-2 Example 1 Write an Equation Given the Slope and a Point 1 Write an equation of a line that passes through (–1, 2) with a slope of . 4 Step 1 Find the y-intercept. y = mx + b Slope-intercept form 1 1 2 = (-1) + b Replace m with 4, y with 2, and x with –1. 4 1 2 = -4 + b Multiply. 1 1 1 1 2 + 4 = -4 + b + 4 Add 4 to each side. 9 4=b Simplify. Step 2 Write the equation in slope-intercept form. y = mx + b Slope-intercept form 1 9 1 9 y = 4x + 4 Replace m with 4 and b with 4. 1 9 Therefore, the equation of the line is y = x + . 4 4 Example 2 Write an Equation Given Two Points Write an equation of the line that passes through each pair of points. a. (8, 6) and (0, 3) Step 1 Find the slope of the line containing the given points. y2 - y1 m= x -x Slope Formula 2 1 3-6 = (x1, y1) = (8, 6) and (x2, y2) = (0, 3) 0-8 -3 3 = -8 or 8 Simplify. Step 2 Use the slope and either of the two points to find the y-intercept. y = mx + b Slope-intercept form 3= 8 (0) + b 3 3 Replace m with 8, x with 0, and y with 3. 3=0+b Simplify. 3=b Simplify. Step 3 Write the equation in slope-intercept form. y = mx + b Slope-intercept form 3 3 y = 8x + 3 Replace m with 8 and b with 3. 3 Therefore, the equation of the line is y = 8x + 3. b. (-2, -7) and (1, 5) Step 1 Find the slope of the line containing the given points. y2 - y1 m= Slope Formula x2 - x1 5 - (-7) = 1 - (-2) (x1, y1) = (-2, -7) and (x2, y2) = (1, 5) 12 = 3 or 4 Simplify. Step 2 Use the slope and either of the two points to find the y-intercept. y = mx + b Slope-intercept form 5 = (4)(1) + b Replace m with 4, x with 1, and y with 5. 5=4+b Simplify. 5–4=4+b–4 Subtract 4 from each side. 1=b Simplify. Step 3 Write the equation in slope-intercept form. y = mx + b Slope-intercept form y = 4x + 1 Replace m with 4 and b with 1. Therefore, the equation of the line is y = 4x + 1. Real-World Example 3 Use Slope-Intercept Form RUNNING In 1975, the World record for the one-mile run was 3 minutes 51 seconds. In 1999, the world record was approximately 3 minutes 43 seconds. Write a linear equation that could be used to estimate the world record time, in seconds, for any year after 1975. Understand You know the time in 1975 is 3 minutes 51 seconds or 231 seconds. You know the time in 1999 is 3 minutes 43 seconds or 223 seconds. Plan Let x represent the year after 1975. Let y represent the time in seconds. Write an equation of the line that passes through the points (0, 231) and (24, 223). Solve Find the slope. y -y m = x2 - x1 Slope formula 2 1 223 – 231 = 24 – 0 Let (x 1 , y 1 ) = (0, 231) and (x 2 , y 2 ) = (24, 223). –8 1 = 24 or –3 Simplify. Choose (0, 231) and find the y-intercept of the line. y = mx + b Slope-intercept form 1 1 231 = –3(0) + b Replace m with -3, x with 0, and y with 231. 231 = b Simplify. 1 Write the equation using m = –3 and b = 231. y = mx + b Slope-intercept form 1 1 y = –3x + 231 Replace m with -3 and b with 231. 1 Therefore, the equation is y = –3x + 231. Check Check your result by using the coordinates of the other point. 1 y = –3x + 231 Original equation 1 223 –3(24) + 231 Replace y with 223 and x with 24. 223 –8 + 231 Multiply. 223 = 223 Simplify. Real-World Example 4 Predict from Slope-Intercept Form RUNNING Use the equation in Example 3 to predict the world record time for the one-mile run in 2008. 1 y = –3x + 231 Original equation 1 y = –3(33) + 231 Replace x with 2008 – 1975 or 33. y = 220 Simplify. Using the equation, an estimate of the world record in 2008 is 220 seconds or 3 minutes 40 seconds.