Cogito
Grade 8 Math · Chapter 3 · Lesson 5
Comparing Lines in Different Forms
A table, a graph, and an equation, side by side.
10 problems · about 19 minutes · 8.F.A.2
What this lesson teaches
The child compares two linear relationships given in different representations.
- Every linear relationship carries a slope and a starting value.
- Both can be pulled out of a table, a graph, an equation, or a description.
- Once both are in that form, comparing them is comparing two pairs of numbers.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Unit Rate as Slope: A proportional line through (7, 28). What is its slope?
Answer 4
Why 4.
Review — Slope from Two Points: Through (1, 2) and (4, 11). Slope?
Answer 3
Why 3.
Review — y = mx + b: y = 3x − 4. What is y when x = 6?
Answer 14
Why 14.
Warm Up
Straightforward practice. Get the method working first.
3 problemsAt x = 0, y = 8; at x = 5, y = 33. What is the slope?
Answer 5
Why 5.
In y = 2x + 9, what is the starting value?
Answer 9
Why The y when x is nought.
In y = −3x + 1, what is the slope?
Answer -3
Why It falls.
Build It Up
The same ideas with more to keep track of.
2 problemsAt x = 0, y = 5; at x = 4, y = 17. What is the slope?
Answer 3
Why 12 ÷ 4.
Of slopes 4 and 6, which relationship grows faster? Give the number.
Answer 6
Why The steeper one.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Equation: In y = 7x + 4, what is the slope?
Answer 7
Why 7.
The Table: At x = 0, y = 12; at x = 3, y = 21. What is the slope?
Answer 3
Why 3.