This document discusses identifying whether lines are parallel, perpendicular, or neither based on their slope and y-intercept characteristics. It provides examples of lines that are parallel because they have the same slope but different y-intercepts, lines that are neither because they have different slopes that are not opposite reciprocals, and rewriting line equations in slope-intercept form to identify lines that are perpendicular because they have opposite reciprocal slopes.

1. PARALLEL, PERPENDICULAR, OR
NEITHER
Practice Problems

2. REMEMBER THE CHARACTERISTICS:
Characteristic Parallel Lines Perpendicular Lines
Slope Same or Equal Opposite Reciprocals
Y-Intercepts Different Same or Different

3. PARALLEL, PERPENDICULAR, OR
NEITHER?
• 𝑦 = 3𝑥 + 2 and 𝑦 = 3𝑥 − 4

4. THESE LINES ARE PARALLEL BECAUSE
THEY HAVE THE SAME SLOPE, BUT
DIFFERENT Y-INTERCEPTS.
The first line has a slope of 3 and a y-intercept of 2.
The second line has a slope of 3 and a y-intercept of -4.

5. PARALLEL, PERPENDICULAR, OR
NEITHER?
• 𝑦 = 3𝑥 − 2 and 𝑦 = −3𝑥 + 4

6. THESE LINES ARE NEITHER BECAUSE THEY
HAVE DIFFERENT SLOPES, BUT THOSE SLOPES
AREN’T OPPOSITE RECIPROCALS.
The first line has a slope of 3 and a y-intercept of -2.
The second line has a slope of -3 and a y-intercept of 4.

7. PARALLEL, PERPENDICULAR, OR
NEITHER?
• 𝑥 + 3𝑦 = 12 and 6𝑥 − 2𝑦 = 12

8. IT WOULD BE EASIER TO DO THIS PROBLEM IF
THE EQUATIONS WERE IN SLOPE-INTERCEPT
FORM, SO BEGIN BY REWRITING THEM.
• 𝑥 + 3𝑦 = 12
• Subtract x on each side:
• 3𝑦 = −𝑥 + 12
• Divide each term by 3:
• 𝑦 = −
1
3
𝑥 + 4
• This line has a slope of −
1
3
and a y-
intercept of 4.
• 6𝑥 − 2𝑦 = 12
• Subtract 6x on each side:
• −2𝑦 = −6𝑥 + 12
• Divide each term by -2:
• 𝑦 = 3𝑥 − 6
• This line has a slope of 3 and a y-
intercept of -6.

9. THESE LINES ARE PERPENDICULAR BECAUSE
THEY HAVE OPPOSITE RECIPROCAL SLOPES.
The first line has a slope of -1/3.
The second line has a slope of 3/1.