Exercise 9 Page 86

Functions where y varies directly with x — direct variation equations — follow a specific format. y= kx In this form, k≠ 0. By substituting the given values for x and y into the equation, we can determine the constant of variation, k.

y=kx

SubstituteII

x= 8, y= 14

14=k( 8)

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Solve for k

RearrangeEqn

Rearrange equation

k(8)=14

DivEqn

.LHS /8.=.RHS /8.

k=14/8

ReduceFrac

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

k=7/4

Now that we have the constant of variation, we can write the function. y= 7/4x 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=12.

y=7/4x

Substitute

x= 12

y=7/4( 12)

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Simplify right-hand side

MoveRightFacToNum

a/c* b = a* b/c

y=7* 12/4

ReduceFrac

a/b=.a /4./.b /4.

y=7* 3/1

DivByOne

a/1=a

y=7* 3

Multiply

Multiply

y=21

For the equation y= 74x, when x=12, the value of y is 21.