Answer:
Part 1) [tex]y=45x+150[/tex]
Part 2) The total charge is [tex]\$1,175[/tex]
Step-by-step 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
[tex]y=mx+b[/tex]
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
[tex]m=45\frac{\$}{hour}[/tex]
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
[tex]b=\$150[/tex]
The linear equation is
[tex]y=45x+150[/tex]
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
[tex]y=45(25)+150[/tex]
[tex]y=\$1,175[/tex]
