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Big Ideas Math: Modeling Real Life, Grade 8

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

Practice Test

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Exercise 7 Page 192

Parallel lines have the same slope.

The red line and the green line are parallel.

Two lines are parallel if their slopes are identical. Let's now consider the given graph.

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 the red line, which passes through ( -4, 1) and ( 2, 4).

m = y_2-y_1/x_2-x_1

SubstitutePoints

Substitute ( -4, 1) & ( 2, 4)

m=4- 1/2-( -4)

Subtract term

m=3/2-(- 4)

a-(- b)=a+b

m=3/2+4

Add terms

m=3/6

a/b=.a /3./.b /3.

m=1/2

The slope of the red line is 12. We will use the same method to identify the slopes of the blue line and the green line.

Line	Points	y_2-y_1/x_2-x_1	Slope
Red	( -4, 1) & ( 2, 4)	4- 1/2-( -4)	1/2
Blue	( -4, - 1) & ( 2, 0.5)	0.5-( - 1)/2-( -4)	1/4
Green	( -2, -4) & ( 2, - 2)	- 2-( -4)/2-( -2)	1/2

Now that we have identified the slope of each line, we can see that the red line and the green line have the same slope, but the slope of the blue line is different. This means the red line and the blue line are parallel.

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