A grocery store sells sliced cheddar cheese by weight. The relationship between the amount of cheddar cheese in pounds, x, and the total cost in dollars of the sliced cheddar cheese, y, is represented by the graph below.
What is the constant of proportionality as shown in the graph?
0
Number of Pounds
Total Cost (in dollars)
x
y
0
Number of Pounds
Total Cost (in dollars)
(6 , 24)
6
18
24
4
The constant of proportionality is found by determining the ratio of the change in the y-values to the change in the x-values. In this case, the change in y-values is 24 - 18 = 6 and the change in x-values is 6 - 0 = 6.
Therefore, the constant of proportionality is 6/6 = 1.
To find the constant of proportionality, we need to determine the ratio between the change in the total cost and the change in the number of pounds.
From the graph, the total cost increases by $24 when the number of pounds increases by 6. So, the change in the total cost is $24 and the change in the number of pounds is 6.
The constant of proportionality (k) is given by:
k = (change in y) / (change in x)
k = ($24) / (6 pounds)
k = $4 / pound
Therefore, the constant of proportionality is $4 per pound.
To find the constant of proportionality from the graph, we need to calculate the slope of the line that represents the relationship between the amount of cheddar cheese in pounds, x, and the total cost in dollars of the sliced cheddar cheese, y.
The equation for slope is:
slope = (change in y) / (change in x)
In this case, we can calculate the slope by choosing two points on the line.
From the given graph, we can see that the coordinates of two points are (0, 0) and (6, 24).
Using these coordinates, the change in y is 24 - 0 = 24, and the change in x is 6 - 0 = 6.
Therefore, the slope or the constant of proportionality can be calculated as:
slope = (24 - 0) / (6 - 0) = 24 / 6 = 4
Hence, the constant of proportionality as shown in the graph is 4.