Question

Nancy created a graph to predict the pay she will take home after taxes are taken from her income. Using the information on the graph, what is the constant of proportionality?

A line graph titled Nancy's Pay has Nancy's Income on the x-axis and Take Home Pay on the y-axis. At 60 dollars of income, she has 48 dollars of take home pay. At 130 dollars of income, she has 104 dollars of take home pay.
a. 0.48
b. 0.6
c. 0.8
d. 1.25

Answer 1

The constant of proportionality for the graph predicting Nancy's take home pay is 0.8, which means for every dollar earned, she takes home $0.80 after taxes. The correct answer is option c. 0.8.

Step-by-step explanation:

To determine the constant of proportionality for the graph Nancy created predicting her take home pay from income, we'll compare her take home pay to her income at the given points. The given points are (60, 48) and (130, 104), where the first number in each pair represents Nancy's income and the second represents her take home pay.

To find the constant of proportionality (k), which is the ratio of take home pay (y) to income (x), in the formula y = kx, we can use either pair of points provided:

• Using the first point (60, 48), k = 48 ÷ 60 = 0.8.
• Using the second point (130, 104), k = 104 ÷ 130 = 0.8.

Therefore, the constant of proportionality is 0.8,

This implies for each dollar Nancy earns, she takes home $0.80 after taxes are deducted, which is option c. 0.8.