Suppose y varies directly with x. Write a direct variation equation that relates x and y. Then find the value of y when x = 7.

1. y = 8 when x = - 4

From the statement, y varies directly with x. It can be expressed as:

y α x

To change it to an equality, we insert a proportionality constant k.

y = kx

We first solve for k,

8 = k (-4)

k = - 2

Therefore, when x = 7,

y = - 2 (7)

y = - 14

For direct variation, y = kx

8 = - 4k

k = 8/-4 = - 2

Therefore, required equation is y = - 2x

when x = 7, y = - 2 (7) = - 14