Question

If y varies inversely as x, and y = 10 when x = 7, find y for the x-value of 10.

Answer 1

\(\bf \begin{array}{cccllll}
\textit{something }&\textit{varies inversely to }&\textit{something else}\\ \quad \\
\textit{something }&=\cfrac{{\color{red}{ \textit{some value }}}}{\textit{something else}}\\ \quad \\
y&=\cfrac{{\color{red}{ n}}}{x}
&&\implies y=\cfrac{{\color{red}{ n}}}{x}
\end{array}
\\ \quad \\
y=10\qquad x=7\qquad 10=\cfrac{{\color{red}{ n}}}{7}\)

solve for "n" to find the "constant of variation"
to find "y" when x = 10

just plug in those values in the original equation, along with the found "n" value to get "y"

Answer 2

so it's 7?

Answer 3

yeap

Answer 4

I need help with one more question

Answer 5

hmmm seems to be 2 pieces of the graph
to the left of 0, is increasing thus is a direct variation
from 0 to the right is decreasing, so is an inverse variation on that side

Answer 6

but if you were to consider only the integer value for "x" regardless of its sign
then yes, it'd be an inverse variation

Answer 7

so it would be inverse

Answer 8

so is that the answer?

Answer 9

well, you'd be correct, is an inverse variation, if only the integer value is used

Answer 10

keep in mind that an inverse variation means, when "x" increases, moves to the right you could say, "y" decreases, goes down towards 0