Question

card 7
two friends have summer jobs. let x
represent the number of hours they worked
and y represent their pay in dollars. which
friend makes the most money per hour?
explain your thinking.
arjun’s graph
kyrie’s table
(graph of arjuns pay with x-axis as hours (0 - 10) and y-axis as pay (0 - 50), a line through origin)
(table for kyrie: x=2,y=16.30; x=4,y=32.60; x=8,y=65.20)

Explanation:

Step1: Find Arjun's hourly pay

Arjun's graph is a line through the origin, so the pay per hour is the slope. From the graph, when \( x = 4 \), \( y = 40 \) (estimating from the line). So slope \( m=\frac{y}{x}=\frac{40}{4} = 10 \) dollars per hour.

Step2: Find Kyrie's hourly pay

Using Kyrie's table, take two points, e.g., \( (2, 16.30) \). The pay per hour is \( \frac{y}{x}=\frac{16.30}{2}=8.15 \) dollars per hour.

Step3: Compare the two rates

Arjun's rate is \( 10 \) dollars per hour, Kyrie's is \( 8.15 \) dollars per hour. Since \( 10>8.15 \), Arjun makes more per hour.

Answer:

Arjun makes the most money per hour because his pay - per - hour rate (calculated as the slope of his pay - hours graph, \( \$10 \) per hour) is greater than Kyrie's pay - per - hour rate (calculated from her pay - hours table, \( \$8.15 \) per hour).