Question

1. Determine whether y varies directly with x. If so, find the constant ofvariation.a. y = -5x

Answer 1

We will investigate whether two variables ( x and y ) varies directly with each other and determine the corresponding constant of variation.

We have the following relation at hand:

`y\text{ = -5x}`

First to determine the whether the relation is "direct" we will resort to the following definition:

`As\text{ x increases, y increases if x decreases then y also decreases}`

We will apply the above definition of " direct " relation to the problem as follows:

`\begin{gathered} x\text{ = 1 then, y = -5} \\ x\text{ = 2 then, y = -10} \\ x\text{ = 3 then, y = -15} \end{gathered}`

We substitute increasing values of ( x ) in the given relation and track the corresponding values of ( y ). We see that as ( x ) increases then ( y ) decreases.

The above result denies the definition of a direct relation. Therefore,

`\textcolor{#FF7968}{y}\text{\textcolor{#FF7968}{ does NOT varies directly with x}}`