Parallel and 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?

• $$y=-\frac{1}{4}x-25$$

• $$y=\frac{1}{4}x+2$$

• $$y=-4x-25$$

• $$y=4x+13$$

• $$y=\frac{1}{4}x+9$$

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

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

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

Write the equation of a line PARALLEL to that passes through the point (3, 1).  $y=-\frac{5}{2}x+10$  

•  $y=-\frac{5}{2}x\ +\ 6$  

•  $y\ =-\frac{5}{2}x+\frac{17}{2}$  

•  $y=\frac{2}{5}x+6$  

•  $y=\frac{2}{5}x+\ 8$  

Multiple Choice

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

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 Select

Select the two lines that are parallel.

• $y=4x-2$

• $y=-\frac{1}{4}x$

• $y=-4x+1$

• None are parallel.

Multiple Select

Select the two lines that are parallel.

• $y=5x-3$

• $x\ +\ 5y=2$

• $-10y-2x=0$

• None are parallel

Multiple Select

Select the two lines that are perpendicular.

• $y=4x-2$

• $y=-\frac{1}{4}x$

• $y=-4x+1$

• None are perpendicular.

Multiple Select

Select the two lines that are perpendicular.

• $2x+6y=-3$

• $-1.5y+4.5x=6$

• $y=-4x+1$

• None are perpendicular.

Multiple Choice

Are these two lines parallel, perpendicular or neither?
y = -1/3x - 5
y = 1/3x + 2

• Parallel
• Perpendicular
• Neither

Multiple Choice

A line is perpendicular to    y = 2x - 7.
What is the slope of this line? 

• -2
• 1/2
• -1/2
• 2

Multiple Choice

Are the lines parallel, perpendicular, or neither?

• Parallel
• Perpendicular
• Neither

Multiple Choice

Two lines that are parallel will have ...

• Slope that is opposite reciprocals

• No slope

• Slope that is the same

• none of the above

Multiple Choice

Two lines that are perpendicular lines have ...

• Slope that is opposite reciprocals

• No Slope

• Slope that is the same

• none of the above

Multiple Choice

What slope is parallel to:  
m = 4

• 4
• -1/4
• -4
• 1/4

Multiple Choice

What slope is perpendicular to:  
m = 5/8

• -5/8
• 5/8
• -8/5
• 8/5

Multiple Choice

A line is parallel to   y = 2x - 7.
What is it's slope?

• -2
• 1/2
• -1/2
• 2