Q64. - Algebra 2

Question

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

Step-by-Step Solution

Answer

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

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 $x=6$ , $y=15$ .