Exercise 70 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= 3, y= 9

9=m( 3)

DivEqn

.LHS /3.=.RHS /3.

3=m

RearrangeEqn

Rearrange equation

m=3

Now that we have the constant of variation, we can write the function. y= 3x 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=3x

Substitute

x= 10

y=3( 10)

Multiply

Multiply

y=30

For the equation y=3x, when x=10, the value of y is 30.