Question

For the data in the table, does 𝑦 vary directly with 𝑥? If it does, write an equation for the direct variation.
the table:
(x | Y)
4 | 11
16 | 22
24 | 33

Answer 1

is it a yes or no

Answer 2

To determine if 𝑦 varies directly with 𝑥, we need to check if the ratio of 𝑦 to 𝑥 remains constant.

Let's calculate the ratio for each pair of values in the table:

For the first pair (4, 11):
𝑦/𝑥 = 11/4 = 2.75

For the second pair (16, 22):
𝑦/𝑥 = 22/16 = 1.375

For the third pair (24, 33):
𝑦/𝑥 = 33/24 = 1.375

Since the ratio of 𝑦 to 𝑥 is consistent (1.375), we can conclude that 𝑦 varies directly with 𝑥.

To find the equation for the direct variation, we can use the formula 𝑦 = 𝑘𝑥, where 𝑘 is the constant of variation.

Using any pair from the table, let's use the first pair (4, 11):
11 = 𝑘 * 4

Solving for 𝑘:
𝑘 = 11/4

The equation for the direct variation is:
𝑦 = (11/4)𝑥

Answer 3

Yes, 𝑦 varies directly with 𝑥.