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
#1:
Instructions: determine if parallel, perpendicular, or neither.
$$a)\hspace{.2em}10x - 2y=-6, 5x - y=12$$
$$b)\hspace{.2em}7x - 3y=15, 3x + 7y=147$$
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#2:
Instructions: determine if parallel, perpendicular, or neither.
$$a)\hspace{.2em}{-}3x - 3y=19, -6x + 6y=38$$
$$b)\hspace{.2em}15x + 19y=21, 3x + 26y=28$$
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#3:
Instructions: write in standard form.
$$a)\hspace{.2em}(-2,-4) $$$$ \text{Parallel to:}$$$$ 4x - y=5$$
$$b)\hspace{.2em}(2,-5) $$$$ \text{Parallel to:}$$$$ 4x + y=-3$$
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#4:
Instructions: write in standard form.
$$a)\hspace{.2em}(1,3) $$$$\text{Parallel to:}$$$$ 3x + 2y=-8$$
$$b)\hspace{.2em}(4,-1) $$$$\text{Perpendicular to:}$$$$ y=\frac{5}{2}x - 2$$
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#5:
Instructions: write in standard form.
$$a)\hspace{.2em}(-3,-2) $$$$\text{Perpendicular to:}$$$$ y=x + 4$$
$$b)\hspace{.2em}(-3,2) $$$$\text{Perpendicular to:}$$$$ y=\frac{1}{2}x - 4$$
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Written Solutions:
#1:
Solutions:
a) Parallel 
b) Perpendicular 
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#2:
Solutions:
a) Perpendicular 
b) Neither 
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#3:
Solutions:
$$a)\hspace{.2em}4x - y=-4$$
$$b)\hspace{.2em}4x + y=3$$
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#4:
Solutions:
$$a)\hspace{.2em}3x + 2y=9$$
$$b)\hspace{.2em}2x + 5y=3$$
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#5:
Solutions:
$$a)\hspace{.2em}x + y=-5$$
$$b)\hspace{.2em}2x + y=-4$$
