Final answer:
The constant of variation for the graph is 3, while for the equation 10x/3y=1, it is (10/3) upon rearrangement. Thus, the equation has a greater constant of variation. Therefore, the correct answer is B).
Step-by-step explanation:
The question refers to the comparison of the constants of variation for a graph and an equation. Constants of variation are essential in understanding the relationship between two variables.
When variables are directly proportional, the constant of variation is the factor by which one variable changes as the other changes.
In the given line graph, the slope, which represents the constant of variation, is given as 3, meaning for every increase of 1 on the x-axis there is a rise of 3 on the y-axis.
The equation 10x/3y=1 can be rearranged to express y in terms of x, yielding y = (10/3)x.
The coefficient of x in this equation also represents the constant of variation, which is (10/3).
Comparing the constant of variation of the graph (3) to that of the equation ((10/3)), we can conclude that the equation has a greater constant of variation because (10/3) is larger than 3.
Therefore, the correct answer is B) The equation has a greater constant of variation.
"Your question is incomplete, probably the complete question/missing part is:"
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).
10x/3y=1.
A) The graph has a greater constant of variation.
B) The equation has a greater constant of variation.
C) The constant of variation is the same for the graph and the equation.
D) The constant of variation cannot be compared because the equation is nonproportional.