The rate of change of the contractor's total earnings in dollars with respect to the number of hours worked is $8.75 per hour.
it is clear from the diagram attached that
fixed amount = $20
earning after he works for 5 hours A= $63.75
earning after he works for 15 hours B= $151.25
earning after he works for 25 hours C= $238.75
B-A = 87.5
C-B = 87.5
It means there is a linear relationship between the amount and working hours.
equation of this linear relationship can be found by a straight line equation
what is the equation of a straight line?
equation of a straight line is
[tex]y =mx+c[/tex]
where m is the slope.
c is the intercept.
so,
[tex]y = \frac{63.75-20}{5-0} x + c\\\\y = \frac{43.75}{5} x+ c\\\\y = 8.75x+c[/tex]
'c' can be found by satisfying any point on the graph
let us say x=0 y=20
c = 20
equation will be:
[tex]y=8.75x + 20[/tex]
rate of change
[tex]\frac{dy}{dx} = 8.75[/tex].
therefore, the rate of change of the contractor's total earnings in dollars with respect to the number of hours worked is $8.75 per hour.
to get more about straight-line refer to:
https://brainly.com/question/4192088
