Question

David keeps records of his monthly earnings. Last month he worked 140 hours and earned $3700. This month he worked 120 hours and earned $3200.

Answer 1

Explanation:

Part A:

Rate of pay for David =
`\frac{\text{Change in earnings}}{\text{Change in hours worked}}`

=
`(3700-3200)/(140-120)`

= $25

Part B:

If he worked for number of hours = x

Then the function representing the earning will be,

f(x) = 25x + b

For an ordered pair (120, 3200),

3200 = 25(120) + b

b = 3200 - 3000

b = 200

Therefore, function will be,

f(x) = 25x + 200

Part C:

"Slope = 25" means the rate of change in earnings per hour is $25.

Similarly, y-intercept 'b = 200' will represent the fixed amount earned by David in addition to the per hour earnings.