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 = 8

1. y = 4 when x = 8

Answer 1

To write a direct variation equation, we use the form y = kx. Substitute the given values to find the value of k. Then substitute x = 81 to find the value of y.

Step-by-step explanation:

To write a direct variation equation that relates x and y, we use the form y = kx, where k is the constant of variation. In this case, we are given that y varies directly with x, so we can write the equation as y = kx.

Given that y = 4 when x = 8, we can substitute these values into the equation to find the value of k:

4 = k(8)

Dividing both sides by 8, we get:

4/8 = k

k = 1/2

So the direct variation equation that relates x and y is y = (1/2)x.

To find the value of y when x = 81, we can substitute x = 81 into the equation:

y = (1/2)(81)

y = 40.5