About Parallel and Perpendicular Lines:

We should know at this point, that two parallel lines have the same slope and that perpendicular lines have slopes that multiply together to give us -1. So in order to determine if we have parallel or perpendicular lines, we can place each line in slope-intercept form: y = mx + b and observe the slope m of each line. If the slopes are the same, we have parallel lines. If the slopes multiply together to give us -1, the lines are perpendicular. Additionally, we will learn how to write the equation of a line given a point on the line and a line that is parallel or perpendicular to the line.


Test Objectives
  • Demonstrate the ability to determine if two lines are parallel lines
  • Demonstrate the ability to determine if two lines are perpendicular lines
  • Demonstrate the ability to write a line in standard form
Parallel and Perpendicular Lines Practice Test:

#1:

Instructions: determine if parallel, perpendicular, or neither.

$$a)\hspace{.2em}10x - 2y=-6, 5x - y=12$$

$$b)\hspace{.2em}7x - 3y=15, 3x + 7y=147$$


#2:

Instructions: determine if parallel, perpendicular, or neither.

$$a)\hspace{.2em}-3x - 3y=19, -6x + 6y=38$$

$$b)\hspace{.2em}15x + 19y=21, 3x + 26y=28$$


#3:

Instructions: write in standard form.

$$a)\hspace{.2em}(-2,-4), parallel \hspace{.2em}to: 4x - y=5$$

$$b)\hspace{.2em}(2,-5), parallel \hspace{.2em}to: 4x + y=-3$$


#4:

Instructions: write in standard form.

$$a)\hspace{.2em}(1,3), parallel \hspace{.2em}to: 3x + 2y=-8$$

$$b)\hspace{.2em}(4,-1), perpendicular \hspace{.2em}to: y=\frac{5}{2}x - 2$$


#5:

Instructions: write in standard form.

$$a)\hspace{.2em}(-3,-2),perpendicular \hspace{.2em}to: y=x + 4$$

$$b)\hspace{.2em}(-3,2), perpendicular \hspace{.2em}to: y=\frac{1}{2}x - 4$$


Written Solutions:

#1:

Solutions:

a) Parallel

b) Perpendicular


#2:

Solutions:

a) Perpendicular

b) Neither


#3:

Solutions:

$$a)\hspace{.2em}4x - y=-4$$

$$b)\hspace{.2em}4x + y=3$$


#4:

Solutions:

$$a)\hspace{.2em}3x + 2y=9$$

$$b)\hspace{.2em}2x + 5y=3$$


#5:

Solutions:

$$a)\hspace{.2em}x + y=-5$$

$$b)\hspace{.2em}2x + y=-4$$