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
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.
To find the constant of variation in a direct variation equation, we need to look at how the values of x and y change in relation to each other. In this case, we can see that as x increases by 4 units (from -4 to 0 to 4), y also increases by 1 unit (from -1 to 0 to 1).
Since the ratio of the change in y to the change in x is always 1/4, the constant of variation in this direct variation equation is one-fourth.