Determine whether y varies directly with x. If so, find the constant of variation and write the function rule.
x, y
32, 16
34, 17
38, 19
What is the function rule? Select the correct choice and fill in any answer boxes in your choice below.
y=
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
To determine whether y varies directly with x, we need to check if the ratio of y to x is constant.
For the given values of x and y:
(16/32) = 0.5
(17/34) ≈ 0.5
(19/38) ≈ 0.5
Since the ratio of y to x is approximately constant (0.5), we can conclude that y varies directly with x.
To find the constant of variation, we can choose any of the given pairs of x and y. Let's use the first pair (32, 16). The constant of variation (k) can be found by dividing y by x:
k = 16/32 = 0.5
Therefore, the function rule is:
y = 0.5x
no
My apologies for the incorrect response.
To determine if y varies directly with x, we need to check if the ratio of y to x is constant for all the given values. Let's calculate the ratios:
For the first pair (32, 16): 16/32 = 0.5
For the second pair (34, 17): 17/34 = 0.5
For the third pair (38, 19): 19/38 = 0.5
Since the ratio of y to x is constant (0.5) for all the pairs, we can conclude that y varies directly with x.
To find the constant of variation, we can choose any of the pairs. Let's use the first pair (32, 16). The constant of variation (k) is the ratio of y to x, so k = 16/32 = 0.5.
Therefore, the function rule is:
y = 0.5x