Question

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

1The 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

Answer 1

The graph represents a straight line passing through the origin (0,0). This indicates that the equation of the line is of the form y = kx, where k is the constant of variation.

To find the value of k, we can choose any point on the line and substitute its coordinates into the equation. Let's use the point (4, 1).

1 = k * 4
k = 1/4

Therefore, the constant of variation is one-fourth.