Question

the table shows how many bottles a machine fills in a certain number of seconds.

time (s)	number of bottles filled
30	600
45	900

part a

which of the following graphs represent the proportional relationship described above?

three graphs are shown here, with axes labeled number of bottles filled (y) and time (s) (x), or similar, with different scales and intercepts

graph(s) that describe the proportional relationship graph(s) that do not describe the proportional relationship

Explanation:

Step1: Find the proportionality constant

The ratio of bottles to time is $\frac{300}{15} = 20$, $\frac{600}{30} = 20$, $\frac{900}{45} = 20$. So the relationship is $y = 20x$ (passes through origin, slope 20).

Step2: Check each graph

• Left graph: At $x=60$, $y=600$ (since $20×60=1200$? No, wait, check the table points: $x=15→y=300$, $x=30→y=600$, $x=45→y=900$. Left graph’s scale: x-axis max 100, y-axis max 1000. Middle graph: x-axis up to 60, y-axis up to 1000; $x=15→y=300$, $x=30→y=600$, $x=45→y=900$ (matches $y=20x$). Right graph has a y-intercept ≠0 (starts above origin), so not proportional.

Answer:

The Middle Graph