Question

Using the graph above identify the constant of proportionality between the number of shirts and how much they cost? Hint: simplify your answer

A. K=80
B. K=20
C. K=10
D. k=8

Answer 1

We conclude that the constant of proportionality between the number of shirts and how much they cost is:

k = 8

Hence, option 'D' is correct.

Explanation:

We know that when 'y' varies directly with 'x', we get

y ∝ x

y = kx

k = y/x

where k is called the constant of proportionality

Given the points

• (10, 80)

• (20, 160)

• (50, 400)

For (10, 80)

substituting y = 80 and x = 10 in the equation

k = y/x

k = 80/10 = 8

For (20, 160)

k = y/x

k = 160/20 = 8

For (50, 400)

k = y/x

k = 400/50 = 8

It is clear that the value of k is the same for all the points.

Thus, the value of k = 8

Therefore, we conclude that the constant of proportionality between the number of shirts and how much they cost is:

k = 8

Hence, option 'D' is correct.