Question

If f(x) varies directly with x and f(x) = 32 when x = –8, then what is f(x) when x = 4?

Answer 1

\(\bf \begin{array}{cccllll}
\textit{something }&\textit{varies directly to }&\textit{something else}\\ \quad \\
\textit{something }&={\color{red}{ \textit{some value }}}&\textit{something else}\\ \quad \\
y&={\color{red}{ n}}&x&\implies y={\color{red}{ n}}x
\end{array}\\ \quad \\
f(x)=y=32\qquad x=-8 \implies y={\color{red}{ n}}x\implies 32={\color{red}{ n}}(-8)\)

find "n"
once you find "n", set x = 4 to get "y"

Answer 2

A direct variation has an equation that looks like this:
y=kx
So plug in 32 for y and -8 for x and find k

Answer 3

4 @Mertsj

Answer 4

Wouldn't it be -4?

Answer 5

Oh! yeah because the 8 is negative! @Mertsj

Answer 6

So now we have this equation:
y=-4x

Answer 7

The problem says to find y when x =4

Answer 8

Can you do that?

Answer 9

I'm a bit confused? @Mertsj

Answer 10

Well, if y = -4x and you know that x = 4, why can't you plug that in and find y?

Answer 11

-8? @Mertsj