Parallel & Perpendicular Lines

Parallel and Perpendicular Lines

Objective: Identify parallel and perpendicular line given the equations.

Multiple Choice

Convert the standard form equation into slope-intercept form.

6x - 7y = -35

• $$y=\frac{7}{6}x-5$$

• $$y=\frac{6}{7}x+5$$

• $$y=\frac{5}{7}x-6$$

• $$y=-\frac{6}{7}x-5$$

Parallel Lines

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

SLOPE of Parallel Lines

In the coordinate plane,

Parallel Lines have the SAME SLOPE

Multiple Choice

REVIEW: What is the slope of the line:  $$y=\frac{2}{3}x+4$$  

• $$\frac{2}{3}$$  

• $$-\frac{2}{3}$$  

• $$\frac{3}{2}$$  

• $$4$$  

• $$-4$$  

In the coordinate plane,

Parallel Lines have the SAME SLOPE

Multiple Select

Which two lines are parallel?

• $$y=\frac{3}{7}x-25$$

• $$y=\frac{3}{7}x+2$$

• $$y=\frac{7}{3}x-25$$

• $$y=3x+13$$

• $$y=7x+9$$

Multiple Select

Which two lines are parallel?

• $$y=-\frac{1}{4}x-25$$

• $$y=\frac{1}{4}x+2$$

• $$y=-4x-25$$

• $$y=4x+13$$

• $$y=\frac{1}{4}x+9$$

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?

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:  $$5x+8y=32$$  

• $$y=\frac{5}{8}x-1$$  

• $$y=-\frac{5}{8}x+13$$  

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

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

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

Perpendicular Lines

Lines that intersect at a right (90 degree) angle

RECIPROCAL

​Simple definition is a fraction flipped.

​EXAMPLE

Multiple Choice

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

• $$\frac{8}{5}$$  

• $$-\frac{8}{5}$$  

• $$-\frac{5}{8}$$  

• $$\frac{5}{8}$$  

SLOPE of Perpendicular Lines

In the coordinate plane, Perpendicular Lines

have slopes that are OPPOSITE RECIPROCALS

Multiple Select

Which two lines are perpendicular?

• $$y=\frac{3}{7}x-25$$

• $$y=-\frac{3}{7}x+2$$

• $$y=-\frac{7}{3}x-25$$

• $$y=3x+13$$

• $$y=7x+9$$

In the coordinate plane, Perpendicular Lines

have slopes that are OPPOSITE RECIPROCALS

What about equations in different forms?

Multiple Choice

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

• $$y=-\frac{5}{6}x-2$$  

• $$y=\frac{5}{6}x+13$$  

• $$y=\frac{6}{5}x+11$$  

• $$y=-\frac{6}{5}x-100$$  

Special Opposite Reciprocal Example

​

​EXAMPLE

​What is the opposite reciprocal of 4?

Multiple Select

Which line(s) are perpendicular to the line:  $$8x+2y=22$$  

• $$y=\frac{1}{4}x-1$$  

• $$y=-\frac{1}{4}x+13$$  

• $$y-12=-\frac{1}{4}\left(x+13\right)$$  

• $$y-5=4\left(x+8\right)$$  

• $$y-2=\frac{1}{4}\left(x+3\right)$$  

Multiple Choice

Slopes of parallel lines are...

• opposite reciprocals.
• opposites.
• the same.
• always 7.

Multiple Choice

Slopes of perpendicular lines are...

• opposite reciprocals.
• opposites.
• the same.
• always 7.

Multiple Choice

y = -2/3x + 2
y = 3/2x + 9
These lines are...

• Parallel
• Perpendicular
• Neither

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

What slope is perpendicular to:  
m = 5/8

• -5/8
• 5/8
• -8/5
• 8/5

Multiple Choice

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

• Parallel
• Perpendicular
• Neither

Multiple Choice

Write the equation of a line PERPENDICULAR to the line y = 3x + 2 that passes through the point (9, -2)

• y = -1/3x - 5

• y = 3x-29

• y = 1/3x -5

• y = -1/3x +1

Multiple Choice

Write the equation of the line PARALLEL to the line y = 4x - 9 that passes through the point (-2, 4)

• y = 4x + 12

• y = -4x -4

• y = -1/4x + 5/2

Multiple Choice

Are line A and line B parallel, perpendicular, or neither if:

line A goes through (-1,2) and (3, -6) and

line B has an equation of 3y = -6x + 9?

• parallel

• perpendicular

• neither

Multiple Choice

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

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

The two lines are _____________________.

• Parallel

• Perpendicular

• Neither

Multiple Choice

y = 3x +2
y = 3x - 3
These lines are...

• Parallel
• Perpendicular
• Neither
• The same line

Multiple Choice

Are Line FG and line KJ parallel, perpendicular, or neither if:

F(–1, 2), G(3, –4), K(–2, –3), and J(4, 1)?

• parallel

• perpendicular

• neither

Multiple Choice

Write the equation of the line PARALLEL to the line y = 4x - 9 that passes through the point (-2, 4)

• y = 4x + 12

• y = -4x -4

• y = -1/4x + 5/2

Multiple Choice

Which of the following lines is PARALLEL to the graph of y = -6x + 3 and goes through the point (-1,4)?

• y=1/6x +25/6

• y = 1/6x + 4

• y = -6x - 2

• y = -6x + 4

Match

Match the following

Parallel lines

Perpendicular lines

Intersecting lines

• Parallel lines

• Perpendicular lines

• Intersecting lines

Match

Match the following opposite reciprocal

• -2/3

• 5/4

• 15/4

• -7/5

3/2

-4/5

-4/15

5/7

• 3/2

• -4/5

• -4/15

• 5/7

Multiple Select

Select ALL of the lines that are PERPENDICULAR to y = 3/4x + 9

• y = 3/4x - 3

• y = -3/4x + 9

• y = -4/3x + 8

• 3y = -4x + 5

• 4y = -3x + 7

Multiple Choice

Write the equation of the line PARALLEL to the line y = 4x - 9 that passes through the point (-2, 4)

• y = 4x + 12

• y = -4x -4

• y = -1/4x + 5/2

Multiple Choice

Line a passes through (0, 3) and (-4, 8)

Line b passes through (0, 5) and (5,9)

Lines a and b 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