Which statement correctly compares the constants of variation for the graph and the equation below?
On a coordinate plane, a line goes through points (0, 0) and (1, 3).
StartFraction 10 x Over 3 y EndFraction = 1
The graph has a greater constant of variation.
The equation has a greater constant of variation.
The constant of variation is the same for the graph and the equation.
The constant of variation cannot be compared because the equation is nonproportional.
The constant of variation is the same for the graph and the equation.
To compare the constants of variation for the graph and the equation, we can rewrite the equation in slope-intercept form (y = mx + b) where m represents the constant of variation.
The given equation, StartFraction 10 x Over 3 y EndFraction = 1, can be rearranged to solve for y:
3y = 10x
y = StartFraction 10 Over 3 x EndFraction
Comparing this equation to the given points on the graph (0, 0) and (1, 3), we can see that the constant of variation is 10/3.
Therefore, the correct statement is: The constant of variation is the same for the graph and the equation.