Slope of Perpendicular and Parallel Lines

Slopes of Parallel & Perpendicular Lines

Dr. Tom Giles

Point-Slope Review with parallel and perpendicular

Parallel Lines have SAME slope

Parallel Lines

• Have the same slope

• Have different y-intercepts

• Never intersect

SLOPE of Parallel Lines

In the coordinate plane,

Parallel Lines have the SAME SLOPE

Multiple Choice

Which line is parallel to the line:  $$5x+6y=12$$  

• $$y=-\frac{5}{6}x-2$$  

• $$y=\frac{5}{6}x+13$$  

• $$y=5x+11$$  

• $$y=-5x-100$$  

Multiple Select

Which lines are parallel to the line:  $$5x+8y=32$$  

• $$y=\frac{5}{8}x-1$$  

• $$y=-\frac{5}{8}x+13$$  

• $$y-12=\frac{5}{8}\left(x+13\right)$$  

• $$y-5=\frac{5}{8}\left(x+8\right)$$  

• $$y-2=-\frac{5}{8}\left(x+3\right)$$  

What about equations in different forms?

​Are y = 2x + 4 and y - 19 = 2(x + 21) parallel?

But...

What about equations in different forms?

​Are y = 2x + 4 and 2x + 5y = 10 parallel?

Perpendicular Lines have OPPOSITE RECIPROCAL slopes.

Has to change.

Flip it and switch signs.

Perpendicular Lines

• Have opposite reciprocal slopes

• Can have the same y-intercept

• Intersect at a 90 degree angle

Multiple Choice

Line 1: (15, 20), (17, 18)

Line 2: (-22, -18), (-20, -16)

The two lines are _____________________.

• Parallel

• Perpendicular

• Neither

Multiple Choice

Line 1: $$\left(-1,\ 2\right),\ \left(2,\ 3\right)$$   Line 2:  $$\left(0,\ 0\right),\ \left(3,\ 1\right)$$   These two lines are ______________________

• Parallel

• Perendicular

• Neither

Multiple Choice

If Jaid and Toni both made 5 dollars an hour but Jaid started with 6 dollars and Toni started with 10 dollars. Will they ever have the same amount of money?

• Yes

• No

Multiple Choice

Which of the following lines goes through the point (0, 4) and is parallel to y = 5x - 3?

• y = 1/5x - 3

• y= 5x - 7

• y = 5x + 4

• y = -5x - 3

Multiple Choice

Which of the following lines goes through the point        (-3, 4) and is perpendicular to  y = 3/2x + 6?

• y = 3/2x - 6

• y = 2/3x + 3

• y = -2/3x - 2

• y = -2/3x + 2

Multiple Choice

Write the equation of a line that passes through the point (2, 6) and is perpendicular to the line y = -4x + 8.

• y = 1/4x + 5.5

• y = 4x + 6

• y = -1/4x + 8

• y = -4x + 8

Multiple Choice

What is the slope of

$$y-2=5(x-7)$$  

• 2

• 5

• 7

• -2

Multiple Choice

What is the starting point of

$$y-2=5(x-7)$$  

• 2, 7

• 7, 2

• -2, -7

• -7,- 2

Multiple Choice

What is the slope of

$$y+3=\frac{1}{5}(x+4)$$  

• 3

• 4

• 1/5

• -3

Multiple Choice

What is the starting point of

$$y+3=\frac{1}{5}(x+4)$$  

• 3, 4

• 4, 3

• -3, -4

• -4, -3

Multiple Choice

True or False

Parallel lines have same slopes.

• True

• False

Multiple Choice

What is the parallel slope of

$$y-4=3\left(x+2\right)$$  

• -4

• 3

• -1/3

• 4

Multiple Choice

Are these lines parallel? $$y=2x+3$$   $$y=-2x+3$$  

• yes

• no

Multiple Choice

Are these lines parallel?

$$y=\frac{1}{2}x+3$$  
$$y=\frac{1}{2}x-3$$  

• yes

• no

Multiple Choice

What is the opposite reciprocal of

$$\frac{3}{5}$$  

• 3/5

• 5/3

• -3/5

• -5/3

Multiple Choice

What is the opposite reciprocal of 2?

• 2/1

• 1/2

• -2/1

• -1/2

Multiple Choice

Which lines have the OPPOSITE RECIPROCAL slopes?

• Parallel

• Perpendicular

Multiple Choice

What is the perpendicular slope of

$$y-7=\frac{2}{3}\left(x+5\right)$$  

• 3/2

• -3/2

• 2/3

• -2/3

Multiple Choice

Are the the two lines perpendicular?

$$y=2x+4$$
$$y=-2x-4$$  

• yes

• no

Multiple Choice

Are the two lines perpendicular?

$$y=5x+4$$   $$y=-\frac{1}{5}x+3$$  

• Yes

• No

To Review

• Parallel lines have the same slope but different y-intercepts

• Perpendicular lines have opposite reciprocal slopes and can have the same y-intercept