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

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.

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:

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

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

$$y = mx$$

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

$$y = \frac{3}{4}x$$

Final Answer