Proportional Power Anchor Chart
Proportional Relationships
How to Tell from Tables, Graphs, and Equations
NC.6.RP • NC.7.RP • NC.8.F
The Golden Rule
What makes it proportional?
A relationship is proportional if there is a constant of proportionality (\(k\)). This means the ratio between the dependent variable (\(y\)) and independent variable (\(x\)) is always the same.
\[ k = \frac{y}{x} \]
\[ y = kx \]
Unit Rate • Constant of Proportionality • Slope
1. Tables
Proportional
| \(x\) | \(y\) | \(y/x\) |
|---|
| 2 | 10 | 5 |
| 4 | 20 | 5 |
| 6 | 30 | 5 |
Constant ratio (\(k=5\)) throughout!
NOT Proportional
| \(x\) | \(y\) | \(y/x\) |
|---|
| 2 | 10 | 5 |
| 4 | 12 | 3 |
| 6 | 14 | 2.3 |
Ratios change! No constant \(k\).
2. Graphs
Proportional
1. Straight Line | 2. Thru Origin (0,0)
(0,0)
NOT Proportional
Misses origin OR is not straight
EMPTY ORIGIN
3. Equations
\(y = kx\)
No addition or subtraction! Just multiplication.
\(y = 3x\)
\(y = \frac{1}{2}x\)
\(y = mx + b\)
The "\(+b\)" is a non-zero starting value.
\(y = 3x \mathbf{+ 4}\)
\(y = 2x \mathbf{- 7}\)
Proportional = Predictable
If you have zero \(x\), you must have zero \(y\)!
Ratio & Proportion
Handout Version • Grade 6-8