Cogito
Grade 8 Math · Chapter 3 · Lesson 2
y = mx + b
The slope and where it starts.
10 problems · about 19 minutes · 8.EE.B.6, 8.F.A.3
What this lesson teaches
The child interprets and uses the equation of a line in slope-intercept form.
- Every line can be written y = mx + b.
- m is the slope and b is where it crosses.
- When b is zero the relationship is proportional.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — 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.
4 problemsy = 3x − 4. What is y when x = 6?
Answer 14
Why 14.
In y = mx + b, what does b tell you?
Answer Where the line crosses the vertical axis.
Why b is the y-intercept.
y = 2x + 7. What is the slope?
Answer 2
Why The number with x.
y = 2x + 7. What is y when x = 0?
Answer 7
Why That is b.
Build It Up
The same ideas with more to keep track of.
2 problemsy = −x + 4. What is y when x = 3?
Answer 1
Why −3 + 4.
y = 5x. Does it pass through the origin?
Answer Yes, b is 0.
Why Nothing is added.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Value: y = 4x + 3. What is y when x = 5?
Answer 23
Why 23.
The Intercept: y = 7x − 2. What is y when x = 0?
Answer -2
Why −2.