Slopes Parallel Perpendicular

Draw

DO NOW MONDAY.
Identify the Triangle Congruence Postulate, when possible.
Write SSS, SAS, ASA, AAS, HL, or not possible on the blank

​Types of Slopes

​There are four types of slopes:

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​Negative slopes move down when read from left to right

​

​Positive slopes move up when read from left to right

​

​Undefined slopes are vertical (straight up and down) lines

​

​Zero slopes are horizontal (straight left-to-right) lines

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Multiple Choice

What kind of slope does this line have?

• positive

• negative

• undefined

• zero

Multiple Choice

What kind of slope does this line have?

• positive

• negative

• undefined

• zero

Multiple Choice

Find the slope of the line.

• -2

• 2

• -1

• 1

Parallel Lines

Lines side by side and having the same distance continuously between them

Exploring Parallel and Perpendicular Lines

Understanding the relationship between parallel and perpendicular lines and their significance in geometry.

Parallel and Perpendicular Lines

SLOPE of Parallel Lines

In the coordinate plane,

Parallel Lines have the SAME SLOPE

In the coordinate plane,

Parallel Lines have the SAME SLOPE

Multiple Choice

Slopes of parallel lines are...

• opposite reciprocals.
• opposites.
• identical.
• always 7.

Multiple Choice

1. Which of the following lines is PARALLEL to the graph of y = -6x + 3 ?

• y=1/6x +25/6

• y = 1/6x + 4

• y = -6x - 2

• y = 6x + 4

Multiple Choice

Are these lines parallel?
y = 12x + 4
y = 12x +14

• YES

• NO

Multiple Choice

Are these lines parallel?

y = (-1/2)x + 1

y = (1/2)x - 5

• YES

• NO

Perpendicular Lines

Lines that intersect at a right (90 degree) angle

Multiple Choice

Which two lines are perpendicular?

• Line A and Line B

• Line B and Line C

• Line A and Line C

RECIPROCAL

​Simple definition is a fraction flipped.

​EXAMPLE

Multiple Choice

What is the reciprocal of:  $$\frac{8}{5}$$  

• $$\frac{8}{5}$$  

• $$\frac{5}{8}$$  

SLOPE of Perpendicular Lines

In the coordinate plane, Perpendicular Lines

have slopes that are OPPOSITE RECIPROCALS

Flip and Switch

In the coordinate plane, Perpendicular Lines

have slopes that are OPPOSITE RECIPROCALS

Multiple Choice

Slopes of perpendicular lines are...

• opposite reciprocals

• opposites

• identical

• reciprocals

Multiple Choice

Which slope is perpendicular to  m = 5/8?

• m = -5/8

• m = 5/8

• m = -8/5

• m = 8/5

• None of these

Multiple Choice

Write the equation of a line PERPENDICULAR to y = -1/3x + 5 and passes

• $$y=\frac{1}{3}x+22$$

• $$y=-\frac{1}{3}x-10$$

• $$y=3x-14$$

Multiple Choice

$$y=\frac{2}{3}x+2$$  

$$y=-\frac{3}{2}x$$  

These lines are...

• Parallel

• Perpendicular

• Neither parallel nor perpendicular

• The same line

Multiple Choice

y = 6x + 2
y = -6x + 2
These lines are...

• Parallel
• Perpendicular
• Neither

Multiple Choice

Are the lines parallel, perpendicular, or intersecting?

y = 2

y = 0

• Parallel

• Perpendicular

• Neither

Multiple Choice

y = 3x + 2

y = 3x - 3

These lines are...

• Parallel

• Perpendicular

• Neither parallel nor perpendicular

• The same line

Multiple Choice

Are these lines perpendicular?

$$y=-\ \frac{1}{4}x+8$$

$$y=4x+2$$

• Yes

• No

Multiple Choice

What does "m" represent in y=mx+b?

• y-intercept
• slope
• macaroni
• nothing

Multiple Choice

Which of these lines are parallel to each other:
1) y = 5x -1
2) y = x/5
3) y= -x/5 +11

• 1 & 2
• 2 & 3
• 1 & 3
• None of them

Multiple Choice

1. Write the equation of a line PARALLEL to  $$y=2x+3$$   that passes through the point (3, 1).

• $$y=2x\ -3$$

• $$y=2x-5$$

• $$y=2x\ +\ 1$$

• $$y=-\frac{1}{2}x+\frac{5}{2}$$

Multiple Choice

2. Write an equation for a line parallel to the line

y = (1/3)x - 4 through (-3, 2)

• y = (2/3)x +3

• y = (-1/3)x + 3

• y = (1/3)x + 3

• y = (-5/3)x + 3

Multiple Choice

3. Write an equation for a line parallel to the line

y = (1/3)x - 4 through (-3, 2)

• y = (2/3)x +3

• y = (-1/3)x + 3

• y = (1/3)x + 3

• y = (-5/3)x + 3

Multiple Choice

4. Write an equation of a line that passes through the point (5,-1) and is parallel to the line y = (-3/5)x -3

• y = (-3/5)x + 2
• y = (-3/5)x -2
• y = (3/5)x + 2
• y = (5/3) + 2

Multiple Choice

5. Write the equation of a line PERPENDICULAR to $$y=-2x+1$$  that passes through the point (2, 3).

• $$y=-\frac{1}{2}x+\frac{1}{2}$$

• $$y=\frac{1}{2}x+2$$

• $$y=-2x+7$$

• $$y=-2x+8$$

Multiple Choice

6. Write the equation of a line PERPENDICULAR to $$y=\frac{1}{3}x-9$$  that passes through the point (-6, 10).

• $$y=\frac{1}{3}x-9$$

• $$y=\frac{1}{3}x+10$$

• $$y=-3x+6$$

• $$y=-3x-8$$

Multiple Choice

7. Write the equation of a line PERPENDICULAR to $$y=\frac{1}{3}x-9$$  that passes through the point (-6, 10).

• $$y=\frac{1}{3}x-9$$

• $$y=\frac{1}{3}x+10$$

• $$y=-3x+6$$

• $$y=-3x-8$$

Multiple Choice

8. What is the equation of a line that is perpendicular to the line
   y = 3x - 6 and passes through the point (15,5).

• y = -3x + 10
• y= 1/3x +10
• y = -1/3x +10
• y = 3x -15