Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
1-3. Quiz
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Exercise 10 Page 184

Parallel lines have the same slope but different y-intercepts. Perpendicular lines have slopes that are opposite reciprocals of one another.

Parallel: None.
Perpendicular: Lines a and b.

Practice makes perfect

Parallel lines have the same slope but different y-intercept. Perpendicular lines have slopes that are opposite reciprocals of one another. Therefore, to determine if the lines are parallel, perpendicular, or neither, we first need to find their slopes using the Slope Formula.

Line Points y_2-y_1/x_2-x_1 Slope Simplified Slope
a ( -2,2) & ( 2,1) 1- 2/2-( -2) -1/4 -1/4
b ( 1, -8) & ( 3,0) 0-( -8)/3- 1 8/2 4
c ( -4, -3) & ( 0,-2) -2-( -3)/0-( -4) 1/4 1/4

These lines have different slopes so they cannot be parallel. We can determine if they are perpendicular by multiplying the slopes. Let's start with lines a and b. -1/4 (4)=- 1 Since the product of the slopes equals -1, the lines are perpendicular. Since the slopes of lines b and c are both positive, the lines are not perpendicular, since its product cannot be negative. Now, let's multiply the slopes of lines a and c. -1/4 ( 1/4 )= - 1/16 Since the product of the slopes does not equal -1, the lines are not perpendicular.