Determine whether y varies directly with x. If so, find the constant of variation and write the function rule. X 68 y 17 72 18 84 21
Does y vary directly with x?
Yes
What is the constant of variation? Select the correct choice and fill in any answer boxes in your choice below.
k= boxed 1/4 (Simplify your answer. Type an integer or a fraction.)
What is the function rule? Select the correct choice and fill in any answer boxes in your choice below. A. ___ y = (Simplify your answer. Use integers or fractions for any numbers in the expression.)
B. There is no function rule.
To determine whether y varies directly with x, we need to check if the ratio between y and x is constant.
For the given data:
When x = 68, y = 17
When x = 72, y = 18
When x = 84, y = 21
To check if the ratios are constant, we can calculate the ratios for each pair of x and y:
17/68 ≈ 0.25
18/72 = 0.25
21/84 = 0.25
Since the ratios are all equal to 0.25, y varies directly with x.
The constant of variation (k) is the ratio of y to x, which is 0.25 or 1/4.
The function rule for direct variation is y = kx. Substituting the value of k, the function rule is:
y = (1/4)x (option A)