Question

The value in dollars, y, of a car x years after it was purchased can be modeled by the function y = 14,000 – 875x. What is the meaning of the y-intercept of the linear model?

The initial value of the car is $14,000.

The average value of the car is $14,000.

The car’s value decreases by $875 each year after it was purchased.

The car’s value decreases by $16 each year after it was purchased.

Answer 1

Answer: Option a) The initial value of the car is 14,000

Step-by-step explanation: we know that

The linear equation into slope intercept form is equal to

`y = mx + b`

where m is the slope

b is the y-coordinate of the y-intercept

Remember that

The y-intercept is the value of y when the value of x is equal to zero

In this problem we have

`y = 14,000 - 875x`

so

The slope is equal to
`m = -875($)/(year)`

The y-intercept is
`b = $14,000`

therefore
`$14,000` is the value of the car for x=0 (initial value)

Answer 2

The initial value of the car is $14,000

Explanation:

The correct answer is "The initial value of the car is $14,000."

In the given linear model y = 14,000 - 875x, x represents the number of years since the car was purchased, and y represents the value of the car in dollars after x years.

The y-intercept is the value of y when x is 0, which means it represents the initial value of the car when it was purchased.

So, in this case, the y-intercept is 14,000, which means that the initial value of the car when it was purchased was $14,000.