Exercise 53 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= 0.5, y= 2.5

2.5=m* 0.5

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Solve for m

WriteAsFrac

Write as a fraction

5/2=m * 1/2

CommutativePropMult

Commutative Property of Multiplication

5/2=1/2 * m

RearrangeEqn

Rearrange equation

1/2 * m=5/2

MoveRightFacToNum

a/c* b = a* b/c

1 * m/2=5/2

IdPropMult

Identity Property of Multiplication

m/2=5/2

MultEqn

LHS * 2=RHS* 2

m/2 * 2=5/2 * 2

FracMultDenomToNumber

a/2* 2 = a

m=5

Now that we have the constant of variation, we can write the function. y=5x Finally, by substituting x=20 into the function, we can find the corresponding y-value.

y=5x

Substitute

x= 20

y=5 * 20

Multiply

Multiply

y=100

For the equation y=5x, when x=20, the value of y is 100.