QuestionFind the constant of variation for the point $(12,9)$ in a direct variation. Options: $\frac{1}{2}$ , $\frac{3}{4}$ , 1, 2.

Studdy Solution

STEP 1

Assumptions1. The point $(12,9)$ is part of a direct variation. . In a direct variation, the equation is of the form $y = kx$ , where $k$ is the constant of variation.

STEP 2

We can find the constant of variation by rearranging the direct variation equation to solve for $k$ .
$k = \frac{y}{x}$

STEP 3

Now, plug in the given values for $x$ and $y$ from the point $(12,9)$ to calculate the constant of variation.
$k = \frac{9}{12}$

STEP 4

implify the fraction to get the constant of variation.
$k = \frac{9}{12} = \frac{3}{4}$ The constant of variation is $\frac{3}{4}$ .

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