Question

The function y = 3.75 + 2.50(x - 3) can be used to determine the cost in dollars for a uber ride of x miles. What is the rate of change of the cost in dollars with respect to the number of miles?

PLEASE EXPLAIN HOW YOU GOT YOUR ANSWER.

Multiple choices:
A. $3.75 per mile
B. $6.25 per mile
C. $4.75 per mile
D. $2.50 per mile

Answer 1

Option D is correct

$2.50 per mile

Explanation:

Slope intercept form:

The equation of line is given by:

y = mx+b .....[1]

where,

m is the slope of the line.

b is the y-intercept

As per the statement:

The function y = 3.75 + 2.50(x - 3)

where, y can be used to determine the cost in dollars for a uber ride of x miles.

Using distributive property:
`a \cdot (b+c) = a\cdot b+ a\cdot c`

we have;

`y = 3.75+2.50x-7.50`

⇒
`y = 2.50x-3.75`

On comparing with [1];

m = 2.50

⇒rate of change of the cost in dollars with respect to the number of miles = $2.50 per mile

therefore, $2.50 is the rate of change of the cost in dollars with respect to the number of miles

Answer 2

The cost of each mile is $2.50.

If you simplify the expression given you will get the following.
y = 3.75 + 2.50(x - 3)
y = 3.75 + 2.50x - 7.50
y = 2.50x - 3.75.

Knowing that x is the number of miles and 2.50 is the number being multiplied by, we know that the cost per mile is 2.50.