Exercise 16 Page 304

Direct variation equations are functions where y varies directly with x. They have 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= 7 12

7 12=m( 3)

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Solve for m

RearrangeEqn

Rearrange equation

m(3)=7 12

MixedToFrac

a bc=a* c+b/c

m(3)=15/2

MultEqn

LHS * 1/3=RHS* 1/3

m=15/2*1/3

MultFrac

Multiply fractions

m=15/6

ReduceFrac

a/b=.a /3./.b /3.

m=5/2

Now that we have the constant of variation, we can write the function. y= 5/2x Finally, we will substitute 12 for x in the above equation to find the y-value.

y=5/2x

Substitute

x= 12

y=5/2( 12)

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Simplify

MoveRightFacToNum

a/c* b = a* b/c

y=5* 12/2

ReduceFrac

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

y=5* 6/1

DivByOne

a/1=a

y=5* 6

Multiply

Multiply

y=30

We have found that y=30 when x=12.