Cogito
Grade 8 Math · Chapter 3 · Lesson 3
Slope from Two Points
Rise over run, from any pair.
10 problems · about 19 minutes · 8.EE.B.6
What this lesson teaches
The child calculates the slope of a line through two given points.
- Slope is the change in y divided by the change in x.
- Subtract the two points in the same order, or the sign flips.
- A falling line has a negative slope; a flat line has slope nought.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — y = mx + b: y = 3x − 4. What is y when x = 6?
Answer 14
Why 14.
Review — Why Slope Is the Same Everywhere: Rise 12, run 4. Slope?
Answer 3
Why 3.
Review — Angle-Angle Similarity: Angles 25° and 95°. What is the third?
Answer 60
Why 60°.
Warm Up
Straightforward practice. Get the method working first.
3 problemsThrough (1, 2) and (4, 11). Slope?
Answer 3
Why 3.
Through (0, 1) and (2, 7). Slope?
Answer 3
Why 6 ÷ 2.
Through (1, 5) and (4, 5). Slope?
Answer 0
Why The y never changes.
Build It Up
The same ideas with more to keep track of.
2 problemsThrough (0, 9) and (3, 0). Slope?
Answer -3
Why −9 ÷ 3.
Through (2, 1) and (5, 10). Slope?
Answer 3
Why 9 ÷ 3.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Rise: Through (0, 0) and (3, 12). What is the slope?
Answer 4
Why 4.
The Fall: Through (2, 10) and (6, 2). What is the slope?
Answer -2
Why −2.