Q18. - Algebra 1

Question

Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve

 

If $y=2$ when $x=-12$, what is y when $x=-4$?

Step-by-Step Solution

Answer

The value of y when $x=-4$ is $\frac{2}{3}.$

Step 1. State the concept of Direct Proportionality.

Direct proportion is a mathematical comparison between two numbers where the ratio of the two numbers is equal to a constant value. The proportion definition says that when two ratios are equivalent, they are in proportion. The symbol used to relate the proportions is "$\propto$".

 

Here y varies directly as x.

 

That is, $y\propto x$

Therefore $y=kx\dots \left(1\right)$

Where, k is a constant.

Step 2. Find the value of ‘ k ’.

Find the value of k by substituting $y=2\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}x=-12$ in equation $y=kx$

$\begin{array}{c}2=k\left(-12\right)\\ \frac{2}{-12}=\frac{-12k}{-12}\\ \frac{1}{-6}=k\\ k=\frac{1}{-6}\left(\text{Equation\hspace{0.17em}\hspace{0.17em}}2\right)\end{array}$

Step 3. Calculate the value of ‘ y ’

Calculate the value of y by substituting $x=-4\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}y=\frac{1}{-6}$ in $y=kx$

$$\begin{gathered} y=\left(\frac{1}{-6}\right)\left(-4\right) \\ y=\frac{2}{3} \end{gathered}$$

Thus, the value of y is $\frac{2}{3}$.