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1 year ago

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A car manufacturer is reducing the number of incidents with the transmission by issuing a voluntary recall. During week 10 of th

e recall, the manufacturer fixed 200 cars. In week 15, the manufacturer fixed 175 cars. Assume that the reduction in the number of cars each week is linear. Write an equation in function form to show the number of cars seen each week by the mechanic

2 answers:

Leviafan [203]1 year ago

8 0

Answer:

f(x) = -5x + 250

Step-by-step explanation:

Digiron [165]1 year ago

7 0

Answer:

f(x) = -5x + 250

Step-by-step explanation:

* Lets explain how to solve the problem

- In week 10 the manufacturer fixed 200 cars

- In week 15, the manufacturer fixed 175 cars

- the reduction in the number of cars each week is linear

- The form of the linear equation is y = mx + c, where m is the slope of

the line which represent the equation and c is the y-intercept

- The slope of the line m = $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

where (x1 , y1) and (x2 , y2) are two points on the line

* Lets solve the problem

- Assume that the weeks' number is x and the cars' number is y

∴ (10 , 200) and (15 , 175) are two points on the line which represent

the linear equation between the cars' numbers and the weeks

numbers

∵ Point (x1 , y1) is (10 , 200) and point (x2 , y2) is (15 , 175)

∴ x1 = 10 , x2 = 15 and y1 = 200 and y2 = 175

- Use the rule of the slope above to find m

∴ $m=\frac{175-200}{15-10}=\frac{-25}{5}=-5$

- Substitute the value of x in the form of the linear equation above

∴ y = -5x + c

- To find c substitute x and y by one the coordinates of one of the

two points

∵ x = 10 when y = 200

∴ 200 = -5(10) + c

∴ 200 = -50 + c

- Add 50 to both sides

∴ 250 = c

- Substitute the value of c by 250

∴ y = -5x + 250, where the number of cars seen each week is y and

x is the number of the week

∵ f(x) = y

∴ f(x) = -5x + 250

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Step 1

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Group terms that contain the same variable, and move the constant to the opposite side of the equation

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Complete the square. Remember to balance the equation by adding the same constants to each side.

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