Question

The value of 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?

a) The initial value of the car is 14,000.
b) The average value of the car is 14,000.
c) The car’s value decreases by $875 each year after it was purchased.
d) The car’s value decreases by $16 each year after it was purchased.

Please help.

Answer 1

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

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)