Question

Find the slope of the line.

y varies directly with x: y = -2 when x = 4. Find the constant of variation. Then find the value of y when x = -1/2.

Answer 1

\(\begin{array}{cccccclllll}
\textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\
\textit{something}&=&{\color{brown}{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\
y&=&{\color{brown}{ n}}&\cdot&x
\\\hline\\
&& y={\color{brown}{ n }}x
\end{array}
\\ \quad \\
\bf y=-2\qquad x=4\quad \implies -2={\color{brown}{ n }}4\impliedby find\ {\color{brown}{ n}}\textit{ or constant of variation}
\)

once you find it, plug it back in the equation and solve when x = -1/2

Answer 2

@jdoe0001 - the constant of variation is -2. so when x = -1/2, y = 1...?

Answer 3

-2? are you sure?

Answer 4

\(\bf y=-2\qquad x=4\quad \implies -2={\color{brown}{ n }}4\implies \square ?={\color{brown}{ n}}\)

Answer 5

I'm confused, sorry. @jdoe0001

Answer 6

well... lemme write it a bit differently

if you have -2 = 4n
what would "n" be?

Answer 7

I think I did it backwards, sorry. Is it -1/2? @jdoe0001

Answer 8

yeap is -1/2

now we know that n = -1/2 thus
what's "y" when x = -1/2?

thus \(\bf y=-2\qquad x=4\quad \implies -2={\color{brown}{ n }}4\implies -\cfrac{1}{2}={\color{brown}{ n}}
\\ \quad \\
y=-\cfrac{1}{2}x\qquad\qquad x=-\cfrac{1}{2}\implies y=-\cfrac{1}{2}\left( -\cfrac{1}{2} \right)
\\ \quad \\
y=-\cfrac{1}{2}\cdot -\cfrac{1}{2}\implies y=\cfrac{-1\cdot -1}{2\cdot 2}\implies y=\cfrac{1}{4}\)

Answer 9

@jdoe0001 - 1/4

Answer 10

minus * minus = positive

Answer 11

@jdoe0001 - I'm sorry if I confused you. I tend to put a "-" when I reply to someone. my answer is 1/4.

Answer 12

heeh tis ok =)