Exercise 48 Page 173

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= 10, y= 15

15=m( 10)

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Solve for m

RearrangeEqn

Rearrange equation

m(10)=15

DivEqn

.LHS /10.=.RHS /10.

m=15/10

ReduceFrac

a/b=.a /5./.b /5.

m=3/2

Now that we have the constant of variation, we can write the function. y=3/2x 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=22.

y=3/2x

Substitute

x= 22

y=3/2( 22)

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Evaluate right-hand side

MoveRightFacToNum

a/c* b = a* b/c

y=3* 22/2

ReduceFrac

a/b=.a /2./.b /2.

y=3* 11/1

DivByOne

a/1=a

y=3* 11

Multiply

Multiply

y=33

For the equation y= 32x, when x=22, the value of y is 33.