Q17. - Algebra 1

Question

Suppose y varies 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 $x=14$?

Step-by-Step Solution

Answer

The value of y when $x=14$ is 35.

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 $y=kx$ … (1)

where k is 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 y is 35.