Question

This graph shows a proportional relationship.

What is the constant of proportionality?
Enter your answer as a ratio in simplified form by filling in the boxes. 2/5 1/2

Answer 1

The constant of proportionality is:

• k = 5/4

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

From the graph, it is clear that the point (2/5, 1/2) passes through the line which represents the direct relationship.

so we have the point (2/5, 1/2), and

x = 2/5

y = 1/2

so substituting x = 2/5 and y = 1/2 in the equation

k = y/x

k = [1/2] / [2/5]

k = [1 × 5 ] / [2 × 2 ]

k = 5/4

Therefore, the constant of proportionality is:

• k = 5/4