Question

the table represents the number of milkshakes sold by a restaurant since they were added to the menu.

time (months)	milkshakes sold
4	380
7	501
10	622
13	744

which graph best represents the relationship between time and the number of milkshakes sold?

choose 1 answer:

a. graph of a straight line with positive slope

b. graph of a curve with increasing slope

Explanation:

Step1: Check rate of change

Calculate the difference in milkshakes sold and time between consecutive data points:

• $\Delta x_1 = 4-1=3$, $\Delta y_1=380-259=121$
• $\Delta x_2 = 7-4=3$, $\Delta y_2=501-380=121$
• $\Delta x_3 = 10-7=3$, $\Delta y_3=622-501=121$
• $\Delta x_4 = 13-10=3$, $\Delta y_4=744-622=122$ (near constant, minor rounding)

Step2: Identify relationship type

Since the change in $y$ (milkshakes sold) is nearly constant for each equal change in $x$ (time), the relationship is linear. A linear relationship is represented by a straight line graph.

Answer:

A. A straight line graph with positive slope starting above the origin