Question

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

If $y=-5$when $x=-2$, what is y when$x=14$?

Short answer

The value of y when$x=14$ is 35.

Step-by-step solution

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 yvaries directly as x.

That is, $y\propto x$

Therefore$y=kx$ … (1)

where kis a constant.

Step 2. Find the value of Constant ‘k’.

Find the value of k by substituting $y=-5\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}x=-2$in equation $y=kx$.

$\begin{array}{c}-5=k.\left(-2\right)\\ \frac{-5}{-2}=\frac{-2k}{-2}\\ \frac{5}{2}=k\\ k=\frac{5}{2}\end{array}$

Step 3. Calculate the value of ‘y’.

Calculate the value of y by substituting $x=14\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}y=\frac{5}{2}$in $y=kx$.

$\begin{array}{c}y=\frac{5}{2}\times 14\\ y=\frac{70}{2}\\ y=35\end{array}$

Thus the value of yis 35.