Question

The equation S = 50 + 45w represents the savings, S, after w weeks working and depositing money into a savings account at the bank. Determine whether there is a proportional relationship and Explain your reasoning. *

Answer 1

Given:

Saving, S, after w weeks is represent by the equation

`S=50+45w`

To find:

Whether there is a proportional relationship.

Solution:

If y is proportional to x, then

`y\propto x`

`y=kx`

where, k is constant of proportionality.

Here, there is no constant term and (0,0) satisfy this equation.

The given equation is

`S=50+45w`

Here, we have a constant term.

For S=0 and w=0,

`0=50+45(0)`

`0=50`

Which is not true as
`0\\eq 50`.

Since, there is a constant term 50 and the equation is not true for (0,0), therefore, the given relationship is not proportional relationship.