Exercise 44 Page 306

Functions where y varies directly with x — direct variation equations — follow a specific format. y= mx In this form, m≠ 0. We can substitute the x- and y-values from the known point, ( 3, 4), into this equation to determine the constant of variation, m.

y=mx

SubstituteII

x= 3, y= 4

4=m* 3

DivEqn

.LHS /3.=.RHS /3.

4/3=m

RearrangeEqn

Rearrange equation

m=4/3

Now that we have the constant of variation, we can write the function. y= 4/3x 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=9.

y=4/3x

Substitute

x= 9

y=4/3* 9

MoveRightFacToNum

a/c* b = a* b/c

y=4* 9/3

SimpQuot

Simplify quotient

y=4* 3

Multiply

Multiply

y=12

The missing value is 12.