Slope Secrets Cheat Sheet Final Plus Plus Plus Plus Plus Plus Plus Plus Plus Plus Plus Plus Plus Plus Plus Plus Plus Plus Plus Plus Plus Plus Plus
SLOPE SECRETS
PART 1: Graphical & Tabular Foundations
STUDENT:
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PERIOD:
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Slope Formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \)
In Plain English "Change in Y over
Change in X"
Delta Symbol \( \frac{\Delta y}{\Delta x} \)
1. From a Graph
Method: Rise Over Run
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- Find 2 "Perfect Corners".
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- Start at the left point.
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- Count UP/DOWN (Rise).
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- Count RIGHT (Run).
RISE (+4) RUN (+4)
\( m = \frac{Rise}{Run} = \frac{4}{4} = 1 \)
2. From a Table
Method: The "Delta" Jump
Pick two rows. Subtract values. Y is always on TOP!
| \( x \) | \( y \) | Jump |
|---|
| 2 | 10 | |
| \( \Delta y = +4 \) | | |
\( \Delta x = +3 \)
|
| 5 | 14 |
Slope (m) = 4 / 3
Line Orientation Guide
Positive
Negative
Zero Slope
Undefined
SLOPE SECRETS
PART 2: Tech Hacks & Context Clues
A.3.B Master Reference
Desmos Table Hack
Instant slope from ANY Table
1
Click + → Table.
2
Type points into x1 and y1.
3
Look below table and click:
ADD REGRESSION
Result \( y_1 \sim mx_1 + b \)
m = 0.625
Fraction
Click the fraction icon next to the result for the exact answer!
Context "Red Flags"
PER
$10 per hour
EACH
$3 each car
EVERY
2 every week
A / AN
$5 a gallon
NEGATIVE CHECK: If the problem says "Decreases", "Loses", "Spends", or "Drops", make the slope Negative (-).
HOY VUX Mnemonics
HOY
H orizontal Line
0 Slope (m=0)
Y = # (Equation)
VUX
V ertical Line
U ndefined Slope
X = # (Equation)
FINAL PRO TIP: Simplify your fraction & check signs!
