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
Parallel Lines Practice Test:

#1:

Instructions: Determine if each pair of lines is parallel, perpendicular, or neither.

a) $$7x + 2y = 10$$ $$4x - 14y = 42$$

#2:

Instructions: Determine if each pair of lines is parallel, perpendicular, or neither.

a) $$2x - 5y = 0$$ $$6x - 15y = -30$$

#3:

Instructions: Write the standard form of the equation of the line described.

a) $$\text{Through:} \, (-3,1)$$ $$\text{Parallel to:}$$$$y = -\frac{1}{3}x - 2$$

#4:

Instructions: Write the standard form of the equation of the line described.

a) $$\text{Through:} \, (1, 5)$$ $$\text{Parallel to:}$$$$y = -\frac{1}{6}x - 2$$

#5:

Instructions: Write the standard form of the equation of the line described.

a) $$\text{Through:} \, (4, -5)$$ $$\text{Perpendicular to:}$$$$y = \frac{8}{5}x - 1$$

Written Solutions:

#1:

Solutions:

a) Perpendicular

#2:

Solutions:

a) Parallel

#3:

Solutions:

a) x + 3y = 0

#4:

Solutions:

a) x + 6y = 31

#5:

Solutions:

a) 5x + 8y = -20