Cogito
Algebra 1 · Chapter 4 · Lesson 4
Parallel and Perpendicular Lines
Same slope, or slopes that multiply to −1.
11 problems · about 22 minutes · G-GPE.B.5
What this lesson teaches
The student identifies parallel and perpendicular lines from their slopes.
- Parallel lines share a slope and differ in intercept.
- Perpendicular slopes are negative reciprocals, so their product is −1.
- Horizontal and vertical lines are perpendicular but escape the product test.
Warm Up
Straightforward practice. Get the method working first.
4 problemsPerpendicular to slope 2. What slope, as a decimal?
Answer -0.5
Why −0.5.
Parallel to y = 3x + 5. What slope?
Answer 3
Why Equal.
Perpendicular to a line of slope 5. What is the perpendicular slope, as a decimal?
Answer -0.2
Why −1 ÷ 5.
Slopes 3 and −1/3. Perpendicular? 1 for yes, 0 for no.
Answer 1
Why Their product.
Build It Up
The same ideas with more to keep track of.
3 problemsSlopes 2 and 2. Parallel? 1 for yes, 0 for no.
Answer 1
Why Equal slopes.
Perpendicular to slope −4. What is the perpendicular slope, as a decimal?
Answer 0.25
Why Flip and change sign.
Match each relationship to its slope condition.
Answer Parallel → Equal slopes, different intercepts; Perpendicular → Slopes multiply to −1; The same line → Equal slopes and equal intercepts
Why The intercept is what separates parallel from identical.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSlopes 4 and −4. Perpendicular? 1 for yes, 0 for no.
Answer 0
Why Their product is −16.
Perpendicular to slope 1. What slope?
Answer -1
Why Flip and negate.
Parallel: Parallel to y = 6x − 2. What slope?
Answer 6
Why 6.
Perpendicular: Perpendicular to y = 2x. What is the product of the two slopes?
Answer -1
Why −1.