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

• $$y=\frac{7}{6}x-5$$

• $$y=\frac{6}{7}x+5$$

• $$y=\frac{5}{7}x-6$$

• $$y=-\frac{6}{7}x-5$$

SLOPE of Parallel Lines

In the coordinate plane,

Parallel Lines have the SAME SLOPE

Multiple Choice

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

• $$\frac{2}{3}$$  

• $$-\frac{2}{3}$$  

• $$\frac{3}{2}$$  

• $$4$$  

• $$-4$$  

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 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?

• $$y=\frac{3}{7}x-25$$

• $$y=-\frac{3}{7}x+2$$

• $$y=-\frac{7}{3}x-25$$

• $$y=3x+13$$

• $$y=7x+9$$

Multiple Choice

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

• $$y=-\frac{5}{6}x-2$$  

• $$y=\frac{5}{6}x+13$$  

• $$y=\frac{6}{5}x+11$$  

• $$y=-\frac{6}{5}x-100$$  

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

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

• $$y=-6x+5$$  

• $$y=-\frac{1}{6}x-3$$  

• $$y=6x+1$$  

• $$y=\frac{1}{6}x-3$$  

Multiple Choice

y = 5/7x +2

y = 5/7x - 30

These lines are...

• Parallel

• Perpendicular

• Neither

Multiple Choice

Write an equation for a line perpendicular to

y = -5x + 3 through (-5, -4)

• y = -3x + 1/5

• y = -3x - 1/5

• y = 1/5x - 3

• y = -1/5x - 3

Multiple Choice

Which is the equation of the line that is PARALLEL to the graph of y = 5x + 7 and has a y-intercept at (0, -2)?

HINT: PLUG (0,-2) AND THE PARALLEL SLOPE INTO y=mx+b. SOLVE FOR b AND REWRITE THE EQUATION IN y=mx+b.

• y = 5x - 2

• y = -2x + 7

• y = 5(x - 2)

• y = -1/5x - 2

Multiple Choice

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

HINT: PLUG (-1,4) AND THE PARALLEL SLOPE INTO y=mx+b. SOLVE FOR b AND REWRITE THE EQUATION IN y=mx+b.

• y=1/6x +25/6

• y = 1/6x + 4

• y = -6x - 2

• y = -6x + 4

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

Are these two lines parallel, perpendicular or neither?

y = -1/3x - 5

y = 1/3x + 2

• 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