Writing Equations Using Two Points 3.3, Exams of Reasoning

Download Writing Equations Using Two Points 3.3 and more Exams Reasoning in PDF only on Docsity! 118 Chapter 3 Writing Linear Equations and Linear Systems STATE STANDARDS MA.8.A.1.1 MA.8.A.1.2 Writing Equations Using Two Points3.3 How can you write an equation of a line when you are given two points on the line? Work with a partner. ● Sketch the line that passes through the given points. ● Find the slope and y-intercept of the line. ● Write an equation of the line. a. 21 4 5 6 7 8 x y −1−2−4 3−3 2 3 5 1 4 6 7 8 9 −3 −2 −1 b. 21 4 5 6 x y −1−2−4 3−3−6 −5 2 3 5 1 4 6 7 8 9 −3 −2 −1 c. 21 4 5 x y −1−2−4 3−3−6−7 −5 2 3 1 4 −3 −4 −5 −6 −7 −8 −2 −1 d. 21 4 5 x y −1−2−4 3−3−6−7 −5 2 3 1 4 5 6 7 −3 −4 −5 −2 −1 ACTIVITY: Writing Equations of Lines1 Section 3.3 Writing Equations Using Two Points 119 Work with a partner. a. You are rising in a hot air balloon. After 1 minute, you are 200 feet above the ground. After 4 minutes, you are 800 feet above the ground. ● Write an equation for the height h in terms of the time t. ● Use your equation to fi nd the height of the balloon after 5 minutes. b. After 5 minutes, the hot air balloon starts to descend. After 6 minutes, you are 200 feet above the ground. ● Write an equation for the height h in terms of the time t. ● Use your equation to estimate when the balloon lands on the ground. c. You are on a roller coaster. After 3 seconds, you are 190 feet above the ground and have reached maximum speed. One second later, you are 95 feet above the ground. ● Write an equation for the height h in terms of the time t. ● When will you reach ground level? ACTIVITY: Writing and Using Linear Equations2 Use what you learned about writing equations using two points to complete Exercises 3 – 5 on page 122. 3. IN YOUR OWN WORDS How can you write an equation of a line when you are given two points on the line? Give an example that is different from those in Activities 1 and 2. 2 4 60 1 3 5 7 8 9 t 100 200 300 400 500 600 700 800 900 1000 0 Time (minutes) H ei g h t (f ee t) h Balloon Ride Balloon Ride 2 4 60 1 3 5 7 8 9 t 100 200 300 400 500 600 700 800 900 1000 0 Time (minutes) H ei g h t (f ee t) h Roller Coaster Ride 2 4 60 1 3 5 7 8 9 t 25 50 75 100 125 150 175 200 225 250 0 Time (seconds) H ei g h t (f ee t) h Exercises3.3 9+(-6)=3 3+(-3)= 4+(-9)= 9+(-1)= 122 Chapter 3 Writing Linear Equations and Linear Systems 1. WRITING Describe how to write an equation of a line using two points on the line. 2. WHICH ONE DOESN’T BELONG? Which pair of points does not belong with the other three? Explain your reasoning. (0, 1), (2, 3) (1, 2), (4, 5) (2, 3), (5, 6) (1, 2), (4, 6) Find the slope and y-intercept of the line that passes through the points. Then write an equation of the line. 3. 2 31 x y −1−2−3 2 3 1 −2 −3 −1 4. 2 31 x y −1−2−3 2 3 1 −2 −3 −1 5. 2 31 x y −1−2−3 2 3 1 −2 −3 −1 Write an equation of the line that passes through the points. 6. (−1, −1), (1, 5) 7. (2, 4), (3, 6) 8. (−2, 3), (2, 7) 9. (4, 1), (8, 2) 10. (−9, 5), (−3, 3) 11. (1, 2), (−2, −1) 12. (−5, 2), (5, −2) 13. (2, −7), (8, 2) 14. (1, −2), (3, −8) 15. ERROR ANALYSIS Describe and correct the error in fi nding the equation of the line that passes through (−1, −6) and (3, 2). 16. JET SKI It costs $175 to rent a jet ski for 2 hours. It costs $300 to rent a jet ski for 4 hours. Write an equation that represents the cost y (in dollars) of renting a jet ski for x hours. 17. CIRCUMFERENCE Consider the circles shown. a. Plot the points (2, 4π) and (3, 6π). b. Write an equation of the line that passes through the two points. Help with Homework 1 slope = rise — run = 8 — 4 = 2 The y-intercept is (0,−4). The equation is y = −4x + 2. ✗ 53 41 x y −1−2−3 2 1 −2 −3 −4 −1 (−1, −6) (3, 2) 3 C = 4 2 π C = 6π Section 3.3 Writing Equations Using Two Points 123 Find the percent of the number. 22. 15% of 300 23. 140% of 125 24. 6% of −75 25. MULTIPLE CHOICE What is the x-intercept of the equation 3x + 5y = 30? ○A −10 ○B −6 ○C 6 ○D 10 18. SOAP BOX DERBY The table shows the changes in elevation for a Soap Box Derby track. a. Draw a Soap Box Derby track in a coordinate plane. b. Does each section of the track have the same slope? Explain. c. Write an equation that represents the elevation y (in feet) of the track between 100 feet and 200 feet. 19. CAR VALUE The value of a car decreases at a constant rate. After 3 years, the value of the car is $15,000. After 2 more years the value of the car is $11,000. a. Write an equation that represents the value y (in dollars) of the car after x years. b. Graph the equation. c. What is the y-intercept of the line? Interpret the y-intercept. 20. WATERING CAN You water the plants in your classroom at a constant rate. After 5 seconds, your watering can contains 58 ounces of water. Fifteen seconds later, the can contains 28 ounces of water. a. Write an equation that represents the amount y (in ounces) of water in the can after x seconds. b. How much water was in the can when you started watering the plants? c. When is the watering can empty? 21. The Leaning Tower of Pisa in Italy was built between 1173 and 1350. a. Write an equation for the yellow line. b. The tower is 56 meters tall. How far off center is the top of the tower? Track Distance Elevation 0 ft 48 ft 100 ft 38 ft 200 ft 28 ft 350 ft 18 ft 600 ft 8 ft 989 ft 0 ft y x 7.75 m (10.75, 42) Leaning Tower of Pisa