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.
(1 point)
Responses
one-fourth
Image with alt text: one-fourth
one-half
Image with alt text: one-half
three-fourths
Image with alt text: three-fourths
1
A direct variation equation can be represented by the equation y = kx, where k is the constant of variation. From the graph you described, the line passes through the origin (0,0) and other points including (-4, -1) and (4, 1).
To find the constant of variation, we can pick any of the points (except the origin), plug the coordinates into the equation y = kx, and solve for k. I'll choose the point (4, 1) for this purpose.
Using y = kx and substituting x = 4 and y = 1, we get:
1 = k * 4
So to find k, we can divide both sides of the equation by 4:
k = 1 / 4
Therefore, the constant of variation, k, is one-fourth.