Question

Write an appropriate direct variation equation if y = 45 when x = 5.

Answer 1

@KeithAfasCalcLover

Answer 2

Direct variation refers to the fact that \((y\phantom{.}\alpha\phantom{.}x)\). That is to say:
\[y=mx\]
Where m is any number. So let us set up the equation:
\[\eqalign{
&y=45\\
&x=5\\
&\\
&y=mx \\
&45=5m \\
}\]
Try solving for \(m\)

Answer 3

y = 9x

Answer 4

Exactly. And just to check, plug in your x and y values:
\[\eqalign{
&y=9x \\
&45=9(5) \\
&45=45
}\]

Since the left side equals the right side, the equation is true!