Delta Dash Activity
GRAPHING SLOPES: \(\frac{\Delta y}{\Delta x}\)
Find Slope from Graphs Using Change in Y over Change in X
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x y 1 2 3 4 1 2 3 Δx = +4 Δy = +2 (0, 1) (4, 3) Slope Triangle
Model Example The Slope Triangle Method \(m = \frac{\Delta y}{\Delta x} = \frac{\text{Vertical Change}}{\text{Horizontal Change}}\)
1. Identify Points
Pick two clean grid points:
\(A(0, 1)\) & \(B(4, 3)\)
2. Count Legs
Vertical: \(\Delta y = +2\)
Horizontal: \(\Delta x = +4\)
3. Write & Simplify
\(m = \frac{+2}{+4} = \mathbf{\frac{1}{2}}\)
Signs: Up \((+\Delta y)\) • Down \((-\Delta y)\) • Right \((+\Delta x)\) • Left \((-\Delta x)\) Simplify fractions to lowest terms!
1 Graph 1 Points Given
2 4 -2 -4 2 4 -2 -4 x y (1, 1) (3, 5)
Vertical \((\Delta y)\):
Horizontal \((\Delta x)\):
Slope \(m = \frac{\Delta y}{\Delta x}\):
2 Graph 2 Points Given
2 4 -2 -4 2 4 -2 -4 x y (-1, 4) (2, -2)
Vertical \((\Delta y)\):
Horizontal \((\Delta x)\):
Slope \(m = \frac{\Delta y}{\Delta x}\):
3 Graph 3 Points Given
2 4 -2 -4 2 4 -2 -4 x y (-2, -2) (2, 0)
Vertical \((\Delta y)\):
Horizontal \((\Delta x)\):
Slope \(m = \frac{\Delta y}{\Delta x}\):
4 Graph 4 Points Given
2 4 -2 -4 2 4 -2 -4 x y (-3, 3) (3, -1)
Vertical \((\Delta y)\):
Horizontal \((\Delta x)\):
Slope \(m = \frac{\Delta y}{\Delta x}\):
Tip: Moving UP gives \(\Delta y > 0\); moving DOWN gives \(\Delta y < 0\). Moving RIGHT gives \(\Delta x > 0\). Page 1 of 2
GRAPHING SLOPES: SPECIAL & ADVANCED LINES
Horizontal, Vertical, Steep, and Open-Choice Lines
Student Name:
Key Slope Cases: Horizontal line: \(\Delta y = 0 \implies m = 0\). Vertical line: \(\Delta x = 0 \implies m = \text{Undefined}\).
Pick any 2 clean grid points!
5 Graph 5 Steep Incline
2 4 -2 -4 2 4 -2 -4 x y (0, -1) (2, 5)
Vertical \((\Delta y)\):
Horizontal \((\Delta x)\):
Slope \(m = \frac{\Delta y}{\Delta x}\):
6 Graph 6 Horizontal Line
2 4 -2 -4 2 4 -2 -4 x y (-3, 3) (2, 3)
Vertical \((\Delta y)\):
Horizontal \((\Delta x)\):
Slope \(m = \frac{\Delta y}{\Delta x}\):
7 Graph 7 Vertical Line
2 4 -2 -4 2 4 -2 -4 x y (-2, 4) (-2, -3)
Vertical \((\Delta y)\):
Horizontal \((\Delta x)\):
Slope \(m = \frac{\Delta y}{\Delta x}\):
8 Graph 8 Choose Any 2 Points
2 4 -2 -4 2 4 -2 -4 x y
Points chosen: \((\quad, \quad)\) & \((\quad, \quad)\)
\(\Delta y\) (Vertical):
\(\Delta x\) (Horizontal):
Slope \(m = \frac{\Delta y}{\Delta x}\):
Summary: Horizontal line \(\Delta y = 0 \implies m = 0\). Vertical line \(\Delta x = 0 \implies m = \text{Undefined}\). Page 2 of 2
