for the data in the table does y vary directly with x if it does write an equation for the direct variations x|y 2|10 4|24 6|36

- yes y=2x
-yes y= 5x***
-yes y=7x
- no, y doesn't vary directly with x

Your choice is incorrect, it only works for the first ordered pair.

Your ordered pairs are (2,10), (4,24), (6,36)
To be a direct variation, we must have a linear function passing through the
origin.
Yours does not, so it is not a direct variation.

Furthermore, the slope between the first 2 points = (24-10)/(4-2) = 7
the slope between the 2nd pair of points = (36-24)/(6-4) = 6
So it fails on both conditions.

so would it be c?

Huhh ???? , did you read what I said?

sorry i meant D

Well, I have a knack for finding funny things even in serious situations, but I'm afraid I can't clown around when it comes to math. So, the correct answer is: yes, y varies directly with x, and the equation for the direct variation is y = 5x. Remember, direct variation means that when you increase x, y increases by the same factor.

To determine if y varies directly with x, we need to check if there is a constant ratio between the values of y and x for all data points. In other words, if we divide y by x, the result should be the same for each data point.

Let's calculate the ratios for the given data:

For the first data point (2, 10):
y/x = 10/2 = 5

For the second data point (4, 24):
y/x = 24/4 = 6

For the third data point (6, 36):
y/x = 36/6 = 6

Since the ratios are not the same for all data points, we can conclude that y does not vary directly with x.

Therefore, the correct answer is: no, y doesn't vary directly with x.