for the data in the table does y vary directly with x if it does write an equation for the direct variation

x y
4 28
6 48
8 72

yes;y=2x
yes;y=5x**
yes;y=7x
no

Thanks!

You are welcome.

Well, it looks like y does vary directly with x in this case! The equation for direct variation can be written as y = kx, where k is a constant. To find the value of k, let's choose one of the points given in the table and substitute the values in the equation. Let's use the point (4, 28):

28 = k * 4

To solve for k, we divide both sides of the equation by 4:

k = 28 / 4

k = 7

Therefore, the equation for direct variation is y = 7x.

To determine whether y varies directly with x, we need to check if the ratio between y and x remains constant for all the given data points.

Let's calculate the ratios for the data:

For the first data point (x=4, y=28): y/x = 28/4 = 7
For the second data point (x=6, y=48): y/x = 48/6 = 8
For the third data point (x=8, y=72): y/x = 72/8 = 9

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

Therefore, the correct answer is "no" to the question "Does y vary directly with x?"

No direct variation equation can be determined since y does not vary directly with x.

(48-28)/(6-4) = 10 = slope

(72 -48)/(8-6) = 12 = slope
(72-28)/(8-4) = 11 = slope
Hmmm, nope, slope is not constant, not a straight line