Parallel and Perpendicular Lines

1
Parallel and Perpendicular Lines
2
Parallel Lines //

• All parallel lines have the same slope.
• Parallel lines will NEVER have the same
  y-intercept.
• The slope of all vertical lines is undefined. (No
  Slope)
• The slope of all horizontal lines is zero.

3
Perpendicular Lines

• Lines that form a 90 Angle.
• Perpendicular Lines CAN have the same y-intercept
  IF that is where they cross.
• Perpendicular Lines have slopes that are negative
  reciprocals.
• This means to change the sign and flip the slope.
• Ex. If line m has a slope of 5, then its
  negative reciprocal is

4
You try it!!

• IF line p has a slope of -2, then a line
  to it has a slope of

• For line n the
• slope is
• the slope is...

REMEMBER Change the sign And Flip it over.
5
Lets compare Vertical and Horizontal Lines.

• Vertical lines are - to horizontal lines.
• AND
• Horizontal lines are - to vertical lines.

6
Examples
So.....
The slope of line "v" is undefined.
The slope is.....
For line "d" if m0
The slope is.....
7
Name the slope of each line, thenGive the
PARALLEL slope and thePERPENDICULAR slope.
Equation m // m m
y 3x 5
7x y 4
y 2
x -4
8
Why do we need to be able to identify the
Parallel Perpendicular Slopes?

• So that we can write equations for new lines.
• Either lines that are Parallel
• OR lines that are Perpendicular

9
Example 5

• HOW?
• 1. Name the slope of the line you are given.
• 2. List the new slope.
• 3. Use the new slope and the point you are given
  in the slope-intercept formula to write a new
  equation.

Like This...
Write an equation that is PARALLEL to the given
line passing through the given point.
5.
New // Equation
10
Example 6
Write an equation that is PARALLEL to the given
line passing through the given point.
6.
To get the Slope, solve For y

• Find the PRGM key on your calculator.
• Select program ASLOPE
• Which option?
• 2 because you have a point and a slope.
• Enter NEW (parallel) slope
• Enter X and Y from your ordered pair

But DIFFERENT Y-int. (b)
Parallel Lines Have SAME Slope (m)
11
7. x 5 (3, 4)

• Choose program ASLOPE
• Option 2
• Name the slope
• Undefined No number value so..
• Name the x coordinate in the ordered pair.

But DIFFERENT Y-int. (b)
x 3
Parallel Lines Have SAME Slope (m)
No y-int, but different x
Both are Undefined
12
8. y 3x 2 (6, -1)
Write an equation that is PERPENDICULAR to the
given line passing through the given point.

• Choose program ASLOPE
• Option 2
• Name the slope of this line but do not type it
  in.
• m 3
• What is perpendicular to 3?
• - 1/3
• type this one in because you are looking for a
  perpendicular equation.
• Enter the X and Y from the ordered pair.

Perpendicular Lines Have OPPOSITE Slope (m)
AND. DIFFERENT Y-int. (b)
13
Example 9
Write an equation that is PERPENDICULAR to the
given line passing through the given point.
9.
To get the Slope, solve For y

• Find the PRGM key on your calculator.
• Select program ASLOPE
• Which option?
• 2 because you have a point and a slope.
• Enter NEW (perpendicular) slope
• Enter X and Y from your ordered pair

Perpendicular Lines Have OPPOSITE Slopes (m)
AND. DIFFERENT Y-int. (b)
14
Example 10
10. y 8 (-2, 8)

• Choose program ASLOPE
• Option 2
• Name the slope
• ZERO but dont enter it yet.
• What is perpendicular to ZERO?
• Undefined has no number value so
• Name the x coordinate in the ordered pair.

Perpendicular Lines Have OPPOSITE Slopes (m)
AND DIFFERENT Y-int. (b)
x -2
No y-int, but x-int.