1. Module 5 Topic 1 More – Applications of Linear Functions

2. Similar Problem: Assume that y varies directly as x. If y = -12 when x = -4, find x when y = 6. Leave your answer in fractional form if needed. y = kx -12 = k(-4) 3 = k so our direct variation equation is y = 3x y= 3x 6 = 3x 2 = x Example 1

3. Similar Problem: The weight of an object on the moon varies directly as its weight on Earth. With all of his gear on, Neil Armstrong weighed 420 pounds on Earth. When he became the first person to step on the moon on July 20, 1969, he weighed 70 pounds. Tara weighs 112 pounds on Earth. What would she weigh on the moon? y= kx (use Neil Armstrong's information to find the direct variation equation). 420 = k(70) 6 = k y= 6x 112 = 6x 18.67 = x so Tara weighed 18.67 pounds on the Moon Example 2

4. Similar Problem: In 1990, people in the United States spent about $385.7 billion on recreation. In 1995, they spent 445.2 billion. Write a linear equation in slope-intercept form to model the amount (in billions of dollars) spent on recreation since 1990. 1990 = 0 1995 = 5 (0, 385.7) and (5, 445.2) Find the slope. (445.2 - 385.7) ÷ (5 - 0) 59.5 ÷ 5 11.9 = slope Now use the slope and either point to find the y-intercept. (I am going to use 1990 and 385.7) y= mx + b 385.7 = (11.9)(0) + b 385.7 = b So the equation of the line is; y= 11.9x + 385.7 Example 3

5. Similar Problem: In 1990, people in the United States spent about $385.7 billion on recreation. In 1995, they spent 445.2 billion. Using a linear equation in slope-intercept form to model the amount (in billions of dollars) spent on recreation since 1990, predict the amount of money spent on recreation in the United States in 2000. Use the equation found in #6. y = 11.9x + 385.7 2000 - 1990 is 10 so plug in 10 for x. y = 11.9(10) + 385.7 y = 504.7 Example 4