Question

What is the constant of proportionality, k, for the data in the table above?

Write an equation for the relationship.

Answer 1

The constant of proportionality is 6.5.

The equation would be y=6.5x

Answer 2

`y=6.5x`

Explanation:

When two variables are directly proportional then:

`\boxed{y \propto x \implies y=kx}`

where k is the constant of proportionality.

The constant of proportionality is the constant value of the ratio between two variables.

Therefore, to find the constant of proportionality, divide a y-value by its corresponding x-value:

`\begin{aligned}\implies y=kx \implies k&=(y)/(x)\\k&=(65)/(10)\\k&=6.5\end{aligned}`

Substitute the found value of k back into the formula to create an equation for the given relationship:

`\implies y=6.5x`