Questions: A direct variation function contains the points (-8,-6) and (12,9). Which equation represents the function? y=-4/3 x y=-3/4 x y=3/4 x y=4/3 x

Transcript text: A direct variation function contains the points $(-8,-6)$ and $(12,9)$. Which equation represents the function? $y=-\frac{4}{3} x$ $y=-\frac{3}{4} x$ $y=\frac{3}{4} x$ $y=\frac{4}{3} x$

Solution

Solution Steps

To find the equation of a direct variation function given two points, we need to determine the slope of the line that passes through these points. The slope is calculated as the change in y divided by the change in x. Once we have the slope, we can write the equation in the form $ y = mx $, where $ m $ is the slope.

Step 1: Calculate the Slope

To find the slope $ m $ of the line that passes through the points $ (-8, -6) $ and $ (12, 9) $, we use the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the coordinates of the points:

\[ m = \frac{9 - (-6)}{12 - (-8)} = \frac{9 + 6}{12 + 8} = \frac{15}{20} = \frac{3}{4} \]

Step 2: Write the Equation

The equation of a direct variation function can be expressed in the form:

\[ y = mx \]

Substituting the calculated slope $ m = \frac{3}{4} $:

\[ y = \frac{3}{4}x \]