Question 114153: A tire company wants to determine how quickly the tread on its tires wears down with average use. Let x represent the number of months the tire was used. Let y represent the thickness of the tire tread, in millimeters. An equation for a line of best fit is shown below.
Y=
- 5
__ x + 20
9
a. What is the slope of this line of best fit? What does the slope mean in the context of this problem?
b. Tina will need to replace her new tires when they have 5 millimeters of tire tread left. According to the line of best fit, for how many months can Tina drive before she needs to replace her tires? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A tire company wants to determine how quickly the tread on its tires wears down with average use. Let x represent the number of months the tire was used. Let y represent the thickness of the tire tread, in millimeters. An equation for a line of best fit is shown below.
Y=
- 5
__ x + 20
9
a. What is the slope of this line of best fit? What does the slope mean in the context of this problem?
---------
slope = -5/9
meaning: tire tread thickness decreases 5 mm for every 9 months of use.
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b. Tina will need to replace her new tires when they have 5 millimeters of tire tread left. According to the line of best fit, for how many months can Tina drive before she needs to replace her tires? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
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Let y = 5 mm; solve for x = # of months of use.
y=(-5/9)x+20
5 = (-5/9)x + 20
(5/9)x = 15
x = 27 months of use
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Cheers,
Stan H.
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