Question

the function y = 3.75 + 1.5(x-1) can be used to determine the cost in dollars for a taxi ride of x miles. what is the rate of change of the cost in dollars with respect to the number of miles?

Answer 1

Answer:

rate of change of the cost in dollars with respect to the number of miles= 1.5

Step-by-step explanation:

We have been given the function y = 3.75 + 1.5(x-1)

Let us simplify this equation

y = 3.75 + 1.5(x-1)

y= 3.75+1.5x-1.5

y = 1.5x+2.25

On comparing this equation withe the slope intercept form y = mx + b, we get

m = 1.5

b = 2.25

here x represents distance in miles and y represents the cost in dollars. So, the  rate of change of the cost in dollars with respect to the number of miles would be equal to the slope of the line.

Thus, we have

rate of change of the cost in dollars with respect to the number of miles

= slope

= 1.5

Answer 2

The rate of change of a function is the slope of the function.

The rate of change of the function is $1.5 per miles

The function is given as:

$\mathbf{y= 3.75 + 1.5(x - 1)}$

Open bracket

$\mathbf{y = 3.75 + 1.5x - 1.5}$

Collect like terms

$\mathbf{y = 1.5x - 1.5 + 3.75}$

$\mathbf{y = 1.5x +2.25}$

A linear equation is represented as:

$\mathbf{y = mx +b}$

Where: m represents the slope

So, by comparison:

$\mathbf{m =1.5}$

Hence, the rate of change of the function is $1.5 per miles

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