Exercise 12 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= 7

7=k( 8)

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Solve for k

RearrangeEqn

Rearrange equation

k(8)=7

DivEqn

.LHS /8.=.RHS /8.

k=7/8

Now that we have the constant of variation, we can write the function. y= 7/8x 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=14.

y=7/8x

Substitute

y= 14

14=7/8x

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Solve for x

MoveRightFacToNum

a/c* b = a* b/c

14=7/8x

MultEqn

LHS * 8=RHS* 8

14* 8=7/8x * 8

Multiply

Multiply

112=x

RearrangeEqn

Rearrange equation

x=112

For the equation y= 78x, when y=14, the value of x is 112.