Question

4. Contractor 3 gives Mrs. Solar the following fee table showing his charges for the contract work. Number of hours Total cost 2 $120 3 $180 4 $240 5 $300 (a) What is the rate of change? What does this mean in a real-world context? (b) What is the y-intercept? What does this mean in a real-world context? (c) Write an equation to represent the total cost, y, given x hours.

Answer 1

PART A:
The rate of change can be found by taking the total cost divided by the number of hours. It's essentially the "slope" of the line.
$120/2 = $60/hour

In the real world, that just means the contractor charges $60 for each hour of work.

PART B:
If you graph the points, it's obvious the y-intercept is 0.

In the real world, that just means the cost is $0 when the contractor does 0 hours of work.

PART C:
The general form of a line (slope-intercept) is:
y = mx + b

We already figured out the slope (m) and the y-intercept (b) in the first two parts, so just plug them in:
y = 60x + 0

We can just drop the last part about adding 0, so the simple equation is:
y = 60x

PART D:
Just plot the points and connect them with a line.