### 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