Question

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

Answer 1

For direct variation, y = kx
8 = -4k
k = 8/-4 = -2

Therefore, required equation is y = -2x

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

Answer 2

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