Answer:
Explanation:
When expressed in the the slope-intercept form of y = mx + b, the slope of the line is m. m can be used to determine whether two lines are Perpendicular, Parallel, or neither by using these rules:
Given two lines in the format of:
y = m1x + b, and
y = m2x + b,
we can use the following rules:
1. Parallel lines have identical slopes. If m1 = m2, then lines 1 and 2 are parallel.
2. Perpendicular lines have slopes that are the negative inverse of each other. . If m1 = - 1/ m2, then lines 1 and 2 are perpendicular.
Key:
Per is Perpendicular
Par is Parallel
N is Neither
1. m = 2, m = -1/2_____Per________________
2. m = 3, m = -3 _____N_________________
3. m = -4, m =-1/4 ____N________________
4. m = 10, m = -.1 _____Per_______________
5. m = 2, m = 3 _______N_______________
6. m = 4/5, m = 8/10____Par________________
Determine whether the pair of lines listed is parallel, perpendicular or neither. Show your work!
7.
y = 14x − 3
y = −4x + 3 Slopes of 14 and - 4: Neither
8. y = 2x − 4
y = −2x + 5 Slopes of 2 and - 2: Neither
9. 3x + y= 5
y = − 13 x+ 2 Slopes of 2 and - 2: Neither
10. 2x + 3x− 6 = 0
y= − 23 x+ 3 The first is not an equation. x = (6/5) : Neither
Given the lines below, create a line that is parallel, one that is perpendicular and one that is neither.
Line
Parallel
Perpendicular
Neither
11. y = 3x + 4
Line y = 3x + 4
Parallel y = 3x + 6
Perpendicular y = -(1/3)x + 4
Neither y = 5x + 4
12. 2x – y = 8
Line: 2x – y = 8
-y = -2x + 8
y = 2x - 8
Parallel y = 2x + 2
Perpendicular y = -(1/2)x - 8
Neither y = x - 7
13. 3x + 4y+ 12 = 0
Line 3x + 4y+ 12 = 0
4y = - 3x - 12
y = -(3/4)x - 3
Parallel y = -(3/4)x + 2
Perpendicular y = (4/3)x - 3
Neither y = -(1/4)x - 3
14. y = 3
Line y = 3 is not a line. It is a point.
Parallel None
Perpendicular None
Neither Yes