Answer:
The fee for 40 hours of his time is $3,125
Step-by-step explanation:
Let
x -----> the number of hours
y ----> the amount in dollars of Antonio;s fee
we have
For x=20, y=1,625 -----> ordered pair (20,1,625)
For x=45, y=3,500) ----> ordered pair (45,3,500)
Find the linear equation
step 1
Find the slope of the line m
The slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{3,500-1,625}{45-20}[/tex]
[tex]m=\frac{1,875}{25}=75\ \$/h[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=75[/tex] and [tex]point(20,1,625)[/tex]
substitute
[tex]y-1,625=75(x-20)[/tex]
Convert to slope intercept form
[tex]y=75x-1,500+1,625[/tex]
[tex]y=75x+125[/tex]
Determine the fee for 40 hours of his time
For x=40 h
substitute in the equation
[tex]y=75(40)+125=\$3,125[/tex]
