What is the constant of proportionality that relates Matthew's earnings, y, to the number of hours he worked, x?
Remember, the constant of proportionality is k = y/x and can be found using any point on the line.
Matthew's Earnings
Earnings (dollars)
114
128
96
80
64
48
16
1 2 3 4 5 6 7 8 9
Time (hours)
(1 point
( so per hour
O $12 per hour
O $15 per hour
To find the constant of proportionality that relates Matthew's earnings to the number of hours he worked, we need to calculate the ratio of earnings to hours for any point on the line.
Let's take the first point on the line, where Matthew earned $114 for working a certain number of hours. Let's assume he worked x hours for this point.
Therefore, we have the equation: 114 = k * x
To solve for k, we divide both sides of the equation by x:
k = 114/x
This equation gives us the constant of proportionality between Matthew's earnings and the number of hours he worked. We can substitute different values for x to find different values of k.
For example, if Matthew worked 8 hours (x = 8), the equation becomes:
k = 114/8
k = 14.25
Hence, the constant of proportionality in this case is $14.25 per hour.