Question

A piano instructor charges students a one time fee for sheet music and an hourly rate for lessons. the graph below shows the total cost for a student who has taken x classes. To increase her number of students, the instructor put a coupon in the local paper offering to waive the one-time fee for new students. What is the value of the coupon
14$
20$
30$
50$

Answer 1

Answer:

Option (2)

Step-by-step explanation:

Relation between fee charged by piano instructor and the lessons has been shown in the graph.

Two points passing through the line are (2, 80) and (4, 140)

Let the one time fee = $b

Hourly charges for the lessons = $x

Equation of the line will be,

y = mx + b

Slope of the line 'm' = $\frac{y_2-y_1}{x_2-x_1}$

m = $\frac{140-80}{4-2}$

m = $\frac{60}{2}$

m = 30

y = 30x + b

For point (2, 80),

80 = 30(2) + b

b = 80 - 60

b = 20

Therefore, one time fee charged by the instructor = $20

Since instructor put a coupon to waive off the one time fee, value of the coupon will be = $20

Option (2) is the answer.