Cogito
Algebra 1 · Chapter 4 · Lesson 2
Slope from Two Points
Rise over run, and what its sign says.
11 problems · about 22 minutes · F-IF.B.6, A-CED.A.2
What this lesson teaches
The student computes slope from two points and interprets its sign and size.
- Slope is the change in y over the change in x.
- Subtract both coordinates in the same order or the sign flips.
- Horizontal lines have slope zero; vertical lines have none.
Warm Up
Straightforward practice. Get the method working first.
4 problemsThrough (0, 2) and (4, 14). Slope?
Answer 3
Why 3.
Through (0, 1) and (3, 10). Slope?
Answer 3
Why 9 ÷ 3.
Through (2, 8) and (6, 0). Slope?
Answer -2
Why −8 ÷ 4.
Through (5, 2) and (5, 9). Does the slope exist? 1 for yes, 0 for no.
Answer 0
Why The run is zero.
Build It Up
The same ideas with more to keep track of.
3 problemsThrough (0, 4) and (8, 4). Slope?
Answer 0
Why Horizontal.
Through (1, 1) and (4, 13). Slope?
Answer 4
Why 12 ÷ 3.
Sort each line by its slope.
Answer Positive: Rises left to right · Negative: Falls left to right · Zero: Perfectly horizontal
Why Read the line left to right.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsOf slopes 2 and 6, which line is steeper? Give the number.
Answer 6
Why More rise per run.
Through (3, 7) and (5, 3). Slope?
Answer -2
Why −4 ÷ 2.
Rising: Through (0, 0) and (2, 8). Slope?
Answer 4
Why 4.
Flat: Through (1, 6) and (9, 6). Slope?
Answer 0
Why 0.