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=x2−x1y2−y1
Substituting the coordinates of the points:
m=12−(−8)9−(−6)=12+89+6=2015=43
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=43:
y=43x
Final Answer
The equation that represents the function is \\(\boxed{y = \frac{3}{4} x}\\).