Question

If y varies directly as x and $y=5$ when$x=2$ , find y when $x=6$.

Short answer

When$x=6,$$y=15$.

Step-by-step solution

Step 1. Given Information.

Given y varies directly as x and $y=5$ when $x=2$.

Step 2. Calculation.

When y varies directly as x, the equation representing this is $y=kx$ where k is any constant.

Plugging the given x and y values to find k:

$\begin{array}{l}y=kx\\ 5=k\left(2\right)\\ k=\frac{5}{2}\end{array}$

Hence the equation representing the variation is $y=\frac{5}{2}x$

Plugging $x=6$ in the equation to find the value of y:

$\begin{array}{l}y=\frac{5}{2}x\\ y=\frac{5}{2}\left(6\right)\\ y=5\left(3\right)\\ y=15\end{array}$

Step 3. Conclusion.

Hence, when $x=6$, $y=15$.