Question

Suppose that y varies directly with x, and y = 2 when x = 16.(a) Write a direct variation equation that relates x and y.Equation: (b) Find y when x = 7.y =

Answer 1

ANSWER:

(a) y = x/8

(b) y = 7/8

STEP-BY-STEP EXPLANATION:

Since y varies directly with x, the form of the equation would be:

$y=kx$

a.

we can calculate the value of k, just like this:

$\begin{gathered} 2=k\cdot16 \\ k=\frac{2}{16} \\ k=\frac{1}{8} \end{gathered}$

Therefore, the equation would be:

$y=\frac{1}{8}x$

b.

Now we calculate when x = 7, like this:

$\begin{gathered} y=\frac{1}{8}\cdot7 \\ y=\frac{7}{8} \end{gathered}$