Question

Simon charges an initial fee plus an hourly fee to repair TVs. The table below shows the amounts Simon charges for the first three hours of repair. What it’s the rate of change? What is the initial fee? Write a linear equation where x represents the number of hours worked and y represents the total fee of repairing the TV.

Answer 1

Rate of change: 25

Initial value: 25

Equation: y = 25x + 25

Explanation:

✔️hours = x

Fee = y

Rate of change (m) = ∆y/∆x

Rate of change (m) = 25/1 = 25

Rate of change (m) = 25

✔️Initial value = y-intercept (b).

To find the initial value, simply substitute (x, y) = (1, 50) and m = 25 into y = mx + b.

Thus:

50 = (25)(1) + b

50 = 25 + b

Subtract 25 from each side

50 - 25 = b

25 = b

b = 25

✔️To write an equation, substitute m = 25 and b = 25 into y = mx + b.

Thus:

y = 25x + 25