Cogito
Integrated Math 1 · Chapter 7 · Lesson 2
Parallel and Perpendicular Lines
What the slopes tell you.
12 problems · about 21 minutes · G-GPE.B.5
What this lesson teaches
The student uses slope to determine whether lines are parallel or perpendicular and writes their equations.
- Parallel lines have equal slopes.
- Perpendicular slopes are negative reciprocals, with product −1.
- Find the required slope first, then use point-slope form.
Warm Up
Straightforward practice. Get the method working first.
5 problemsA line has slope 3. What is the perpendicular slope, to two decimal places?
Answer -0.33
Why About −0.33.
What is the product of two perpendicular slopes?
Answer Negative one.
Why −1.
Slope 2. Perpendicular slope, as a decimal?
Answer -0.5
Why Flip and negate.
Slope 5. Parallel slope?
Answer 5
Why Equal.
Slope −0.5. Perpendicular slope?
Answer 2
Why Flip and negate.
Build It Up
The same ideas with more to keep track of.
3 problemsSlopes 3 and −1/3. What is their product?
Answer -1
Why That is the test.
Slopes 2 and 2. Parallel or perpendicular? 1 parallel, 2 perpendicular.
Answer 1
Why Equal slopes.
Slope 1. Perpendicular slope?
Answer -1
Why Flip 1 and negate.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsPut the steps for writing a perpendicular line in order.
Answer 1. Read the slope of the given line. 2. Flip it and change its sign. 3. Substitute that slope and the given point into point-slope form. 4. Rearrange into slope-intercept form.
Why The new slope is found before any point is used.
Slope 0.25. Perpendicular slope?
Answer -4
Why Flip and negate.
The Perpendicular: A line has slope 4. What is the perpendicular slope, as a decimal?
Answer -0.25
Why −0.25.
The Parallel: A line has slope −3. What slope is parallel to it?
Answer -3
Why −3.