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Big Ideas Math: Modeling Real Life, Grade 8

BI

Big Ideas Math: Modeling Real Life, Grade 8 View details

2. Slope of a Line

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Exercise 24 Page 153

Parallel lines have the same slope.

See solution.

Practice makes perfect

Two lines are parallel if their slopes are identical. Knowing this, let's start by labeling the lines.

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 a, which passes through ( -2, 3) and ( -5, -2).

m = y_2-y_1/x_2-x_1

SubstitutePoints

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

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

a-(- b)=a+b

m=-2-3/-5+2

Add and subtract terms

m=-5/-3

- a/- b=a/b

m=5/3

The slope of line a is 53. We will use the same method to identify the slopes of lines b and c.

Line	Points	y_2-y_1/x_2-x_1	Slope
a	( -2, 3) & ( -5, -2)	-2- 3/-5-( -2)	5/3
b	( 1, 2) & ( -2, -2)	-2- 2/-2- 1	4/3
c	( 4, 1) & ( 1, -3)	-3- 1/1- 4	4/3

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

Subchapter links

Try It p.149-150

Self-Assessment for Concepts & Skills p.150

Self-Assessment for Problem Solving p.151

Review & Refresh p.152

Concepts, Skills, & Problem Solving p.152-154