Question

8. For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation.

(1 point)
Responses

yes; y = 2x
yes; y = 2 x

yes; y = 5x
yes; y = 5 x

yes; y = 7x
yes; y = 7 x

no; y does not vary directly with x.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine if y varies directly with x, we can check if the ratio between y and x remains constant. Let's look at the data in the table:

x | y
2 | 4
3 | 6
4 | 8
5 | 10

If we calculate the ratio y/x for each pair:
4/2 = 2
6/3 = 2
8/4 = 2
10/5 = 2

Since the ratio is constant (2), y varies directly with x. Therefore, the equation for direct variation is y = 2x.

So, the correct response is:
yes; y = 2x