Question

A computer programmer charges $45 an hour for a coding projects plus a start-up fee of $150.

*Write an equation in slope-intercept form to represent the total cost, y, of a project that takes x hours.

*How much does the programmer charge for a coding project that takes 25 hours?

Answer 1

Part 1)
`y=45x+150`

Part 2) The total charge is
`\$1,175`

Explanation:

Part 1) Write an equation in slope-intercept form to represent the total cost, y, of a project that takes x hours

Let

x ----> the number of hours

y ----> the total cost

we know that

The equation of the in slope intercept form is

`y=mx+b`

where

m is the slope

b is the y-coordinate of the y-intercept

In this problem we have that the charge of $45 an hour for a coding projects is equal to the slope m of the linear equation

so

`m=45(\$)/(hour)`

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

In this problem the y-intercept is the total cost when the number of hours is equal to zero (the y-intercept is the start-up fee of $150)

so

`b=\$150`

The linear equation is

`y=45x+150`

Part 2) How much does the programmer charge for a coding project that takes 25 hours?

For x=25 hours

substitute in the linear equation and solve for y

`y=45(25)+150`

`y=\$1,175`