Exercise 13 Page 356

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= -2/5, y= -3

-3=m( -2/5)

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Solve for m

MoveLeftFacToNum

a*b/c= a* b/c

-3=(m)(-2)/5

MultEqn

LHS * 5=RHS* 5

-15=m(-2)

DivEqn

.LHS /-2.=.RHS /-2.

-15/-2=m

DivNegNeg

- a/- b=a/b

m=15/2

Now that we have the constant of variation, we can write the function. y=15/2x 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 x when y=45.

y=15/2x

Substitute

y= 45

45=15/2x

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Simplify

MoveRightFacToNum

a/c* b = a* b/c

45=15x/2

MultEqn

LHS * 2=RHS* 2

45(2)=15x

Multiply

Multiply

90=15x

DivEqn

.LHS /15.=.RHS /15.

90/15=x

CalcQuot

Calculate quotient

6=x

RearrangeEqn

Rearrange equation

x=6

For the equation y= 152x, when y=45, the value of x is 6.