Question

Is the equation $\mathrm{y}=-15\mathrm{x}$ a direct variation, if so what is the constant of variation?

Answer 1

Step-1: Check whether the equation is direct variation:

If an equation is a direct variation, it must pass through the origin i.e., $(0,0)$.

Given, $\mathrm{y}=-15\mathrm{x}$

Now, if $\mathrm{x}=0$

Then, $\mathrm{y}=-15\left(0\right)$

$\Rightarrow$ $\mathrm{y}=0$

Thus the given equation passes through origin.

Therefore, the given equation is a direct variation.

Step-2: Find the constant of variation:

If an equation is a direct variation, it is of the form $\mathrm{y}=\mathrm{kx}$, where $\mathrm{k}$ is a constant.

So, constant of variation is $\mathrm{k}=\frac{\mathrm{y}}{\mathrm{x}}$

Thus, for given equation, $\mathrm{k}=\frac{-15\mathrm{x}}{\mathrm{x}}$

$\Rightarrow$ $\mathrm{k}=-15$

Hence, $\mathrm{y}=-15\mathrm{x}$ is a direct variation with constant of variation $\mathrm{k}=-15$