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

User Lang
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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}}

User Nawang
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