Question

The variables xx and yy vary directly. use the values to find the constant of proportionality, kk. then write an equation that relates xx and yy. write any fractions in simplest form. y=45; x=40

Answer 1

an equation that relates x and y :

y = 1.125x

Explanation:

The direct variation says that:

`y \propto x`

then equation is of the form:

`y = kx` where k is the constant of variation.

As per the statement:

The variables x and y vary directly.

then by definition we have;

`y = kx` .....[1]

Given that: y = 45 and x = 40

Substitute these in [1] to solve for k;

`45=40k`

Divide both sides by 40 we have;

`1.125 = k`

Therefore, an equation that relates x and y :

y = 1.125x

Answer 2

Direct variation means that changes in x will result to changes in y. If x increase, y also increases and vice versa.

y = kx
k = y / x

y = 45 ; x = 40

k = 45/40
k = 1.125

y = 1.125x

y will increase by 1.125 interval of x.