Exercise 10 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= 30, y= 6

6=k( 30)

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Solve for k

RearrangeEqn

Rearrange equation

k(30)=6

DivEqn

.LHS /30.=.RHS /30.

k=6/30

ReduceFrac

a/b=.a /6./.b /6.

k=1/5

Now that we have the constant of variation, we can write the function. y= 1/5x 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=15.

y=1/5x

Substitute

x= 15

y=1/5( 15)

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Simplify right-hand side

MoveRightFacToNum

a/c* b = a* b/c

y=1* 15/5

ReduceFrac

a/b=.a /5./.b /5.

y=1* 3/1

DivByOne

a/1=a

y=1* 3

Multiply

Multiply

y=3

For the equation y= 15x, when x=15, the value of y is 3.