Jevonte is making lemonade from concentrate. The relationship between the number of quarts of concentrate, x, and the number of quarts of water, y, is represented by the graph below.
What is the constant of proportionality as shown in the graph?
Amount of Water (in quarts)
y axis (numbers)
30
27
24
21
18
15
12
9
6
3
(0,0)
Amount of Concentrate (in quarts)
x axis (numbers)
3, 6, 9, 12, 15, 18, 21, 24, 27, 30
A. 4/3
B. 4/7
C. 3/7
D. 1/5
To determine the constant of proportionality, we can calculate the ratio of the number of quarts of water to the number of quarts of concentrate for each point on the graph.
Looking at the graph, we can see that for every 3 quarts of concentrate, there is 9 quarts of water. This gives us a ratio of 9/3 or 3/1.
We can also see that for every 6 quarts of concentrate, there is 18 quarts of water. This gives us a ratio of 18/6 or 3/1.
Similarly, for every 9, 12, 15, 18, 21, 24, 27, and 30 quarts of concentrate, we have ratios of 3/1.
Since the ratios remain constant at 3/1 for all points on the graph, the constant of proportionality is 3/1 or 3.
Therefore, the correct answer is:
C. 3/7