1. Parallel and Perpendicular Lines Ms. Houghton Geometry Honors
Unit 3
Parallel and Perpendicular Lines Ms. Houghton Geometry Honors

2. Vocabulary Skew Lines Collinear Transversal Parallel Lines
Two lines that will never intersect
The slopes are the same
Perpendicular Lines
Two lines that intersect to form 4 right angles
The slopes are negative reciprocals
Negative reciprocal means the sign changes and the fraction flips.
Skew Lines
2 lines that will not intersect only because they are on 2 different planes
Collinear
Points on the same line
Transversal
Any line that intersects 2 parallel lines

3. Parallel Lines What do we know about parallel lines?
Are the following lines parallel?
Y=3x+5
Y=3x-2
Y=(-5/3)x+2
Y=(5/3)x-3
Y=4x-5
3y-5x=5
Y+5=4x
4y+8x-3=0
Y-3x=5
Y=3
4y+12x=8
X=4

4. Create a line parallel to…
Create an equation for a line parallel to y = 4x - 5 that goes through the point (4,2)
What is the basic form of the equation?
y = mx+b
What does the slope have to be?
Slope must = 4
What do we know?
y =4x + b
Do we know b(y-intercept)?
Do we know y? x?
y = 2 and x = 4

5. Create a line parallel to…
2=4(4)+B
2=16+B
-14 = B
Now rewrite the equation
Y=MX+B
Y=4X-14
Ask yourself is Y=4X-14 parallel to Y=4X+5

6. Your turn
Find the equation of a line that parallel to y = -3x-4 that goes through the point (8,2)

7. Perpendicular Lines What do we know about perpendicular lines?
Decide if the following are perpendicular
Y=2x+2
Y=-2X+2
Y=(1/3)x-4
Y=3x+2
Y=4x-1
Y=4x-9
Y=(-1/4)x+4
Y=(4/1)x-9
Y=(-3/2)x+8
Y=x-1
Y=(2/3)x-2
Y=(-x)+5

8. Create a line perpendicular to…
Create an equation for a line that is perpendicular to the line y=4x+1 that goes through the point (6,-2)
What is the basic form of the equation?
y = mx + b
What does the slope have to be?
m = -1/4
Do we know the y-intercept?
Do we know y? x?
y = -2 and x =6

9. Create a line perpendicular to…
-2=(-1/4)(6)+B
-2= -3/2 +B
4/3 = B
Y=MX+B
Y=(-1/4)X+(4/3)

10. Your Turn
Find the equation of a line perpendicular to y + 3x = 1 that goes through the point (1, 4)