Math 8B U4: Graphing Linear Equations Unit Test 8 of 15

Question

Piper and Carson took summer jobs. The graph represents Piper's earnings in dollars, y
, for working x
hours and the table represents Carson's earnings in dollars, y
, for working x
hours. Who earns more per hour? How much more per hour is made?
They make the same per hour.
They make the same per hour. - no response given

Carson; $21.00 more an hour
Carson; $21.00 more an hour - no response given

Carson; $4.20 more an hour
Carson; $4.20 more an hour - correct

Piper; $20.00 more an hour
show your work

Answer 1

To determine who earns more per hour, we can compare the rates of change of their earnings per hour.

For Piper:
From the graph, we can see that when Piper works 5 hours, she earns $42.
When Piper works 10 hours, she earns $84.

The rate of change for Piper is:
(84 - 42) / (10 - 5) = 42 / 5 = $8.40 per hour

For Carson:
From the table, we can see that when Carson works 5 hours, he earns $58.80.
When Carson works 10 hours, he earns $100.20.

The rate of change for Carson is:
(100.2 - 58.8) / (10 - 5) = 41.4 / 5 = $8.28 per hour

Therefore, Piper earns $8.40 an hour and Carson earns $8.28 an hour. To find out how much more Carson earns per hour than Piper, we can subtract their rates of change:
$8.40 - $8.28 = $0.12

Carson earns $0.12 more per hour than Piper.