About Parallel Lines:
When we have two parallel lines, the slopes will be the same, but the y-intercepts will be different. When we have perpendicular lines, the product of the slopes will be -1. To determine if we have parallel or perpendicular lines, place each line in slope-intercept form and inspect the slopes.
Test Objectives
- Demonstrate an understanding of parallel and perpendicular lines
- Demonstrate the ability to determine if a pair of lines are parallel
- Demonstrate the ability to determine if a pair of lines are perpendicular
- Demonstrate the ability to find the equation of a line given a point and the slope
#1:
Instructions: Determine if each pair of lines is parallel, perpendicular, or neither.
a) $$7x + 2y = 10$$ $$4x - 14y = 42$$
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#2:
Instructions: Determine if each pair of lines is parallel, perpendicular, or neither.
a) $$2x - 5y = 0$$ $$6x - 15y = -30$$
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#3:
Instructions: Write the standard form of the equation of the line described.
a) $$\text{Through:} \, (-3,1)$$ $$\text{Parallel to:}$$$$y = -\frac{1}{3}x - 2$$
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#4:
Instructions: Write the standard form of the equation of the line described.
a) $$\text{Through:} \, (1, 5)$$ $$\text{Parallel to:}$$$$y = -\frac{1}{6}x - 2$$
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#5:
Instructions: Write the standard form of the equation of the line described.
a) $$\text{Through:} \, (4, -5)$$ $$\text{Perpendicular to:}$$$$y = \frac{8}{5}x - 1$$
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Written Solutions:
#1:
Solutions:
a) Perpendicular
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#2:
Solutions:
a) Parallel
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#3:
Solutions:
a) x + 3y = 0
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#4:
Solutions:
a) x + 6y = 31
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#5:
Solutions:
a) 5x + 8y = -20
