Exercise 18 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= - 5, y= 125

125=m( - 5)

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Solve for m

RearrangeEqn

Rearrange equation

m(- 5)=125

DivEqn

.LHS /(- 5).=.RHS /(- 5).

m=125/- 5

MoveNegDenomToFrac

Put minus sign in front of fraction

m=-125/5

CalcQuot

Calculate quotient

m=- 25

Now that we have the constant of variation, we can write the function. y= - 25x Finally, we will substitute 12 for x to find the y-value.

y=- 25x

Substitute

x= 12

y=- 25( 12)

Multiply

Multiply

y=- 300

We have found that y=-300 when x=12.