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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

8. Slopes of Parallel and Perpendicular Lines

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Exercise 10 Page 201

Parallel lines have the same slope.

Yes, see solution.

Practice makes perfect

Two lines are parallel if their slopes are identical.

We have been given two points on each line, so we have enough information to calculate their slopes using the Slope Formula. m=y_2- y_1/x_2- x_1 Note that when choosing points to substitute for ( x_1, y_1) and ( x_2, y_2), it does not matter which points on the line we choose, since the result will be the same. Let's start with line l_1, which passes through ( -2, 5) and ( -3, 1).

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( -2,5) & ( -3,1)

m=1- 5/-3-( -2)

▼

Simplify right-hand side

a-(- b)=a+b

m=1-5/-3+2

Add and subtract terms

m=-4/-1

- a/- b=a/b

m=4/1

a/1=a

m=4

The slope of line l_1 is 4. We will use the same method to identify the slope of line l_2.

Line	Points	y_2-y_1/x_2-x_1	Slope
l_1	( -2, 5) & ( -3, 1)	1- 5/-3-( -2)	4
l_2	( 1, 2) & ( 0, -2)	-2- 2/0- 1	4

Now that we have identified the slope of each line, we can see that l_1 and l_2 have the same slope, so they are parallel.

Subchapter links

Lesson Check p.201

Practice and Problem-Solving Exercises p.201-204

Standardized Test Prep p.204

Mixed Review p.204