Question

The equation y=750x represents the number of dollars y Olivia earns in x weeks. Determine if there is a constant of variation. If so explain what it represents

Answer 1

There is a constant of variation in the equation and it is 750. This means that the amount olivia earns increases by $750 every week.

Explanation:

Given the equation y = 750x which represents the number of dollars y Olivia earns in x weeks, from the equation, it can be inferred that the number of dollars olivia earns is DIRECTLY PROPORTIONAL to the number of weeks. This relationship is therefore a direct variation.

In direct variation, increase in a variable will lead to corresponding increase in the other variable and vice versa by a factor known as the constant of variation.

For example if y is directly proportional to x, it is written mathematically as shown;

`y\alpha x`

`y=kx\\`

`k = y/x`

where k is the constant of proportionality.

comparing the general expression above with the equation in question,

y = 750x

k = 750

Therefore we can conclude that there is a constant of variation in the equation and it is 750. This means that the amount olivia earns increases by $750 every week.