Exercise 69 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= 4, y= 8

8=m( 4)

DivEqn

.LHS /4.=.RHS /4.

2=m

RearrangeEqn

Rearrange equation

m=2

Now that we have the constant of variation, we can write the function. y= 2x 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=2x

Substitute

x= 10

y=2( 10)

Multiply

Multiply

y=20

For the equation y=2x, when x=10, the value of y is 20.