How to find inverse variation

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ACT Math › How to find inverse variation

Questions 1 - 5

Two numbers and vary inversely, and when . If this is true, what is the value of when ?

If when , and the variation is direct, then . Using this, we know that if , $x= \frac{24}{6} = 4$ .

Find the inverse equation of:

$\frac{2x+20}{3}=y$

$\frac{3x-20}{2}=y$

$\frac{1}{2}x+10=y$

$\frac{2x-20}{3}=y$

To solve for an inverse, we switch x and y and solve for y. Doing so yields:

$\frac{3x-20}{2}=y$

Find the inverse equation of .

$y=\frac{4x+18}{5}$

$x=\frac{4y+18}{5}$

$y=\frac{x+18}{4}$

$y=\frac{4x+5}{18}$

1. Switch the and variables in the above equation.

2. Solve for :

$\frac{5y}{5}=\frac{4x+18}{5}$

$y=\frac{4x+18}{5}$

$\begin{matrix} & \x\ & \y\ & \ & \ & \end{matrix}$ When , .

When , .

If varies inversely with , what is the value of when ?

If varies inversely with , $y=\frac{K}{x}$ .

1. Using any of the two combinations given, solve for :

Using :

$18=\frac{K}{2}$

2. Use your new equation $y=\frac{36}{x}$ and solve when :

$y=\frac{36}{12}=3$

If varies inversely with , what is the value of ?

An inverse variation is a function in the form: or $y = \frac{k}{x}$ , where is not equal to 0.

Substitute each $\left ( x,y \right )$ in .

Therefore, the constant of variation, , must equal 24. If varies inversely as , must equal 24. Solve for .