Question

yu yan earns extra money working on weekends. she creates a graph showing the number of hours she works and the amount of money she earns each weekend.

a. based on the graph, does the amount of money yu yan earns appear to be proportional to the number of hours she works? explain how you know.

b. the next weekend, yu yan adds the point (0, 0) to the graph. what does the point (0, 0) mean in this context?

c. how much money does yu yan earn if she works only 1 hour? explain.

Explanation:

Step1: Check proportionality

For two - variables to be proportional, the ratio of the dependent variable (earnings) to the independent variable (hours) should be constant. Let's assume the points on the graph are (2, 20), (4, 40), (6, 50). The ratios are: For (2, 20), $\frac{20}{2}=10$; for (4, 40), $\frac{40}{4} = 10$; for (6, 50), $\frac{50}{6}=\frac{25}{3}
eq10$. Since the ratios are not the same, the amount of money is not proportional to the number of hours.

Step2: Interpret (0, 0)

The x - value represents the number of hours worked and the y - value represents the earnings. The point (0, 0) means that if Yu Yan works 0 hours, she earns 0 dollars.

Step3: Find hourly rate

Since the relationship is not proportional, we can't use a single constant of proportionality. But if we assume a linear relationship based on the first two points (2, 20) and (4, 40), the slope (which is the hourly rate) $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{40 - 20}{4 - 2}=\frac{20}{2}=10$. So she earns 10 dollars per hour if we consider the linear part of the relationship.

Answer:

a. No, because the ratios of earnings to hours are not constant.
b. It means that if Yu Yan works 0 hours, she earns 0 dollars.
c. 10 dollars, assuming a linear relationship based on the first two points where the slope (hourly rate) is 10 dollars per hour.