Question

Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
X Y
7 11
8 13
9 15
10 17

I’m not quite sure how to answer this and I’m super behind on work.

Answer 1

To have a direct variation your data values must satisfy the equation of the form
y = kx or k = y/x
In other words you must get the same value of k for each ordered pairs.
Let's take a look:
for (7,11) , k = 11/7
but for (8,13), k = 13/8 ≠ 11/7

so you do NOT have a direct variation.
Here is a short clip where you do find a direct variation.
Compare the two results.
https://www.youtube.com/watch?v=RLpmnRPtp0s

Answer 2

Thanks!