Question

A landscaper charges customers a one time fee and an hourly rate of $25. For 3 hours of work, it charges $95

- I need the identity ​point​ in​ the scenario

- Write the equation in point-slope​ form

- write the equation in slope-intercept​ form

- Write the equation in standard form

Answer 1

C = 20 + 25h ..... Required identity

(C - 20) = 25(h - 0) ..... Point-slope form

C = 25h + 20 ..... Slope-intercept form.

25h - C = - 20 .... Standard form.

Explanation:

A landscaper charges customers a one time fee and an hourly rate of $25.

If for 3 hours of work, it charges $95.

Then, C = C' + 25h ......... (1)

Where C is the total charge, C' is the fixed charge and h is the number of hours he works.

Therefore, putting C = $95 and h = 3, we get from equation (1),

95 = C' + 75

⇒ C' = 20

Therefore, the equation (1) becomes C = 20 + 25h

Hence, this is the identity in the scenario. (Answer)

Now, the point-slope form of the equation is (C - 20) = 25(h - 0)

where slope is 25 and the point is (0,20).

Now, C = 25h + 20

is the slope-intercept form having slope 25 and y-intercept 20.

Now, the standard form of the equation is 25h - C = - 20 (Answer)