Exercise 128 Page 512

Two lines are parallel if their slopes are identical. Since the given equations are not in slope-intercept form, let's rewrite them so that it will be easier to identify the slopes. Let's start with the line 5x-3y=11.

5x-3y=11

SubEqn

LHS-5x=RHS-5x

- 3y=- 5x+11

DivEqn

.LHS /(- 3).=.RHS /(- 3).

y=- 5/- 3x+11/- 3

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Simplify

DivNegNeg

- a/- b=a/b

y=5/3x+11/- 3

MoveNegDenomToFrac

Put minus sign in front of fraction

y=5/3x+ ( - 11/3 )

AddNeg

a+(- b)=a-b

y=5/3x-11/3

The slope of the given line is 53. We will use the same method to identify the slopes of the lines in given options.

Option	Equation	Slope-Intercept Form	Slope
A	5x-3y=4	y=5/3x-4/3	5/3
B	5x+3y=- 2	y=- 5/3x-2/3	- 5/3
C	3x-5y=11	y=3/5x-11/5	3/5
D	3x+5y=- 1	y=- 3/5x-1/5	- 3/5

Now that we have identified the slope of each line, we can see that the line in option A has the same slope as the given line, so they are parallel.