Question

What is the constant of proportionality of y to x?

Answer 1

Answer: k=2.5

Explanation:

1. As you can see in the graph, when x increases, y also increases at the same rate, therefore, it is a direct proportion that has the following form

`y=kx`

2. Choose one of the points shown in the graph, substitute it into the expression and solve for k, which is the constant of proportionality, as following:

`10=k*4\\k=2.5`

Answer 2

2.5

Explanation:

We are given a graph with a positive slope where the value of y increases when the value of x increases.

For the given graph, we are to find the constant of proportionality of y to x which is the slope of the given line.

We know the formula of the slope =
`\frac{y_2-y_1} {x_2-x_1}`

Substituting the given values in the formula:

`(15-10)/(6-4) = (5)/(2) = 2.5`