Exercise 55 Page 270

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= 0.25, y= 2.6

2.6=m* 0.25

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Solve for m

RearrangeEqn

Rearrange equation

0.25m=2.6

MultEqn

LHS * 4=RHS* 4

0.25m * 4=2.6 * 4

CommutativePropMult

Commutative Property of Multiplication

0.25 * 4 * m =2.6 * 4

Multiply

Multiply

1 * m =10.4

IdPropMult

Identity Property of Multiplication

m=10.4

Now that we have the constant of variation, we can write the function. y=10.4x 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=1.125.

y=10.4x

Substitute

x= 1.125

y=10.4* 1.125

Multiply

Multiply

y=11.7

For the equation y=10.4x, when x=1.125, the value of y is 11.7.