How can you write an equation of a line when you are given the slope and the y-intercept of the line? ACTIVITY: Writing Equations of Lines

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1 . Writing Equations in Slope-Intercept Form How can ou write an equation of a line when ou are given the slope and the -intercept of the line? ACTIVITY: Writing Equations of Lines Work with a partner. Find the slope of each line. Find the -intercept of each line. Write an equation for each line. What do the three lines have in common? a. 7 b. x x Writing Equations In this lesson, ou will write equations of lines in slope-intercept form. c. 8 7 d. x x 78 Chapter Graphing and Writing Linear Equations

2 ACTIVITY: Describing a Parallelogram Math Practice Analze Givens What do ou need to know to write an equation? Work with a partner. a. Find the area of each parallelogram. Write an equation that represents each side of each parallelogram. b. x 7 x ACTIVITY: Interpreting the Slope and the -Intercept Work with a partner. The graph shows a trip taken b a car, where t is the time (in hours) and is the distance (in miles) from Phoenix. a. Find the -intercept of the graph. What does it represent? b. Find the slope of the graph. What does it represent? c. How long did the trip last? d. How far from Phoenix was the car at the end of the trip? e. Write an equation that represents the graph. Distance (miles) Car Trip t Time (hours). IN YOUR OWN WORDS How can ou write an equation of a line when ou are given the slope and the -intercept of the line? Give an example that is different from those in Activities,, and.. Two sides of a parallelogram are represented b the equations = x + and = x +. Give two equations that can represent the other two sides. Use what ou learned about writing equations in slope-intercept form to complete Exercises and on page 8. Section. Writing Equations in Slope-Intercept Form 79

3 . Lesson Lesson Tutorials Stud Tip EXAMPLE After writing an equation, check that the given points are solutions of the equation. Writing Equations in Slope-Intercept Form Write an equation of the line in slope-intercept form. a. b. 7 (0, ) (, ) x Because the line crosses the -axis at (0, ), the -intercept is. So, the equation is = x +. (0, ) (, ) x Find the slope and the -intercept. m = x x 0, or slope -intercept Find the slope and the -intercept. m = x x 0, or Because the line crosses the -axis at (0, ), the -intercept is. slope -intercept So, the equation is = x + ( ), or = x. Exercises 0 Write an equation of the line in slope-intercept form... (0, ) (, ) x (0, ) x (, ) 80 Chapter Graphing and Writing Linear Equations

4 Remember EXAMPLE The graph of = a is a horizontal line that passes through (0, a). Writing an Equation Which equation is shown in the graph? A = B = C = 0 D = x Find the slope and the -intercept. The line is horizontal, so the change in is 0. change in m change in x 0 = 0 x (, ) (0, ) Because the line crosses the -axis at (0, ), the -intercept is. So, the equation is = 0x + ( ), or =. The correct answer is A. EXAMPLE Engineers used tunnel boring machines like the ones shown above to dig an extension of the Metro Gold Line in Los Angeles. The new tunnels are.7 miles long and feet wide. Real-Life Application The graph shows the distance remaining to complete a tunnel. (a) Write an equation that represents the distance (in feet) remaining after x months. (b) How much time does it take to complete the tunnel? a. Find the slope and the -intercept. change in m change in x 000 = 00 Because the line crosses the -axis at (0, 00), the -intercept is 00. So, the equation is = 00x b. The tunnel is complete when the distance remaining is 0 feet. So, find the value of x when = 0. = 00x + 00 Write the equation. 0 = 00x + 00 Substitute 0 for. 00 = 00x Distance remaining (feet) Subtract 00 from each side. 7 = x Divide each side b 00. It takes 7 months to complete the tunnel. 000 (0, 00) Tunnel Digging (, 00) x Time (months) Exercises. Write an equation of the line that passes through (0, ) and (, ).. WHAT IF? In Example, the points are (0, 00) and (, 00). How long does it take to complete the tunnel? Section. Writing Equations in Slope-Intercept Form 8

5 . Exercises Help with Homework. PRECISION Explain how to find the slope of a line given the intercepts of the line.. WRITING Explain how to write an equation of a line using its graph. 9+(-)= +(-)= +(-9)= 9+(-)= Write an equation that represents each side of the figure.. x. x Write an equation of the line in slope-intercept form.. (, ) (0, ) x. (, ) (0, 0) x 7. (0, ) (, ) x 8. (0, ) x (, ) 9. x (0, ) (, ) 0. (, ) x (0, ). ERROR ANALYSIS Describe and correct the error in writing an equation of the line.. BOA A boa constrictor is 8 inches long at birth and grows 8 inches per ear. Write an equation that represents the length (in feet) of a boa constrictor that is x ears old. = x + x (0, ) (, 0) 8 Chapter Graphing and Writing Linear Equations

6 Write an equation of the line that passes through the points.. (, ), (0, ). (, 0), (0, 0). (0, ), (, ). WALKATHON One of our friends gives ou $0 for a charit walkathon. Another friend gives ou an amount per mile. After miles, ou have raised $.0 total. Write an equation that represents the amount of mone ou have raised after x miles. 7. BRAKING TIME During each second of braking, an automobile slows b about 0 miles per hour. a. Plot the points (0, 0) and (, 0). What do the points represent? b. Draw a line through the points. What does the line represent? c. Write an equation of the line. 8. PAPER You have 00 sheets of notebook paper. After week, ou have 7% of the sheets left. You use the same number of sheets each week. Write an equation that represents the number of pages remaining after x weeks. 9. The palm tree on the left is 0 ears old. The palm tree on the right is 8 ears old. The trees grow at the same rate. a. Estimate the height (in feet) of each tree. b. Plot the two points (x, ), where x is the age of each tree and is the height of each tree. c. What is the rate of growth of the trees? d. Write an equation that represents the height of a palm tree in terms of its age. ft Plot the ordered pair in a coordinate plane. (Skills Review Handbook) 0. (, ). (, ). (0, ). (, 7). MULTIPLE CHOICE Which of the following statements is true? (Section.) A The x-intercept is. B The x-intercept is. C The -intercept is. D The -intercept is. x Section. Writing Equations in Slope-Intercept Form 8