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 $0\neq 50$.

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