Mrs.D Math · 8th Grade

ORIGIN
STORY

Slope & Y-Intercept · Proportional vs Nonproportional
📈 Slope
📍 y-intercept
✅ Proportional
❌ Nonproportional
🎯 y = kx → through (0, 0)
📍 y = mx + b → b ≠ 0
📊 y ÷ x constant? Proportional!
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📚 Proportional vs Nonproportional

The Big Idea

Proportional → y = kx → the line passes through the origin (0, 0)

Nonproportional → y = mx + b with b ≠ 0 → the line crosses the y-axis somewhere else.

1
On a graph: Look where the line crosses the y-axis. Through (0, 0)? Proportional. Anywhere else? Nonproportional.
y = 2x → proportional    y = 2x + 3 → nonproportional
2
In a table: Check the ratio y ÷ x for every pair. Same every time? Proportional!
(2, 6), (4, 12), (6, 18) → ratio 3 every time → proportional
3
Watch out! Tables here never show x = 0. If the ratio changes, find b by working backward: b = y − mx.
(2, 7), (4, 11) → m = 2, b = 7 − 2·2 = 3 → nonproportional

How to Play

📈
Graphs — Read the graph and its equation. Decide: proportional or not, and what is b?
📋
Tables — No x = 0 given! Test the ratio or work backward to find b.
🆕
Mixed — Both types together for the ultimate challenge!
🧮
Calculator — New this year! Tap the gold 🧮 button bottom-left any time. Try it in your head first, then verify.
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