Mrs.D Math · 8th Grade

STRAIGHT
TALK

Slope & Y-Intercept · Describing Functions
📈 Functions
✍️ f(x)
📏 Linear
🌀 Nonlinear
📏 y = mx + b
🌀 y = x² + 1
✍️ f(x) = y
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📚 Describing Functions

Linear Functions

y = mx + b  →  a straight line

A function that can be written as y = mx + b is a linear function. A function can be written f(x) for y.

1
From the video: y = 2x + 4 is linear.
x: 0, 2, 4, 6  →  y: 4, 8, 12, 16 (constant rate!)
2
f(x) notation: f(x) = 2x + 4 means the same thing. f(3) = 2(3) + 4 = 10.
3
In a table: linear means y changes by the same amount for each equal step in x.

Nonlinear Functions

If a function cannot be written in the form y = mx + b, it is a nonlinear equation and is not a linear function.

✓
From the video: y = x² + 1 is nonlinear.
x: 1, 2, 3, 4 → y: 2, 5, 10, 17 (rate changes: +3, +5, +7)
✓
Watch for exponents on x like x² or x³ — those make a curve, not a line.

How to Play

🧮
Equations — Spot linear vs. nonlinear equations and evaluate f(x). Choose from 4 answers.
📊
Tables — Match tables to their rule, find missing values, and describe the pattern.
🔀
Mixed — Both types together for the ultimate challenge!
🧮
Calculator — New for 8th grade! Tap the gold 🧮 button any time. Try it in your head first — then verify! 💡
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