Question

If y varies directly as x and $y=14$, when $x=3$. Find the equation that relates x and y.

Short answer

The equation that relates x and y is$y=\frac{14}{3}x$.

Step-by-step solution

Step 1. Given information

Given that If y varies directly as x and $y=14$, when$x=3$.

Equation relating x and y.

Since y varies directly as x, therefore

$$\begin{gathered} y\alpha x \\ \Rightarrow y=kx\to \left(1\right),wherekistheproportionalitycons\tan t. \end{gathered}$$

Now since $y=14$when $x=3$, therefore form equation (1), we get

$$\begin{gathered} 14=k·3 \\ \Rightarrow k=\frac{14}{3} \end{gathered}$$

Now put $k=\frac{14}{3}$in equation (1), we get

$y=\frac{14}{3}x$