Question

Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.

Answer 1

The general equation of direct variation is

y = kx,

where k is a constant.

To see if the given points are a direct variation, try a few points in the equation above. If you get the same value of k every time, it is direct variation. If not, then it isn't.

Let's start with x = 7, y = 11

y = kx

11 = k * 7

k = 11/7

For the first point, we get k = 11/7. For a direct variation, you must get k = 11/7 for every point you try.

Now let's try point (8, 13).

y = kx

13 = k * 8

k = 13/8

13/8 is not equal to 11/7, so since the value of k is different for different ordered pairs, it is not direct variation.