Exercise 20 Page 304

Direct variation equations are functions where x varies directly with y. 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= -1/2, y= 9 13

9 13=m( -1/2)

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Solve for m

RearrangeEqn

Rearrange equation

m(-1/2)=9 13

MixedToFrac

a bc=a* c+b/c

m(-1/2)=28/3

MultEqn

LHS * (- 2)=RHS* (- 2)

m=28/3 (- 2)

MoveRightFacToNum

a/c* b = a* b/c

m=- 56/3

MoveNegNumToFrac

Put minus sign in front of fraction

m=-56/3

Now that we have the constant of variation, we can write the function. y= -56/3x Finally, we will substitute 12 for x to find the y-value.

y=-56/3x

Substitute

x= 12

y=-56/3 * ( 12)

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Simplify

MoveRightFacToNum

a/c* b = a* b/c

y=-56* 12/3

ReduceFrac

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

y=-56* 4/1

DivByOne

a/1=a

y=- 56* 4

Multiply

Multiply

y=- 224

We have found that y=- 224 when x=12.