Exercise 68 Page 314

Functions where y varies directly with x — direct variation equations — follow a specific format. y= mx In this form, m ≠ 0. By substituting the given values for x and y into the equation, we can determine the constant of variation, m.

y=mx

SubstituteII

x= 1, y= 5

5=m( 1)

IdPropMult

Identity Property of Multiplication

5=m

RearrangeEqn

Rearrange equation

m=5

Now that we have the constant of variation, we can write the function. y= 5x With this equation, we can find any value of x or y when we are given the other. In this case, we are looking for y when x=10.

y=5x

Substitute

x= 10

y=5( 10)

Multiply

Multiply

y=50

For the equation y=5x, when x=10, the value of y is 50.