The equation of the line on the graph below is a direct variation equation. What is the constant of variation?
The graph of a line on a coordinate grid is shown connecting the points left-parenthesis negative 4 comma negative 1 right-parenthesis, the origin, and left-parenthesis 4 comma 1 right-parenthesis.
Let's first find the slope of the line passing through the points (-4, -1) and (4, 1). The formula for finding the slope is given by:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates of the two points, we have:
m = (1 - (-1)) / (4 - (-4))
m = 2 / 8
m = 1/4
Since the equation of the line is a direct variation equation, the constant of variation is equal to the slope of the line. Therefore, the constant of variation is 1/4.