Slope Sleuth Guided Notes
Algebra 1 • Linear Functions
SLOPE SLEUTH: FINDING SLOPE FROM A GRAPH
Name:
Date: Period:
What is Slope? (The Core Idea)
Slope measures the steepness and direction of a line on a coordinate plane. It describes the constant rate of change between two variables. In algebra, slope is always represented by the letter m.
The Slope Formula
\(m = \frac{\text{rise}}{\text{run}} = \frac{\Delta y}{\Delta x}\)
1. The 4 Types of Slope (Direction Guide)
Always read graphs from LEFT to RIGHT ➔
Positive Slope
Rises Up (\(m > 0\))
Uphill hike: +
Negative Slope
Falls Down (\(m < 0\))
Downhill ski: -
Zero Slope
Horizontal (\(m = 0\))
Flat ground: 0 fun
Undefined
Vertical Line
Cliff drop: Crash! (div by 0)
2. The 3-Step Sleuth Protocol: Graph to Slope
1
Pick 2 "Clean" Points Locate lattice points where grid lines cross cleanly.
2
Count the RISE (\(\Delta y\)) Count vertical change: UP = (+), DOWN = (-).
3
Count the RUN (\(\Delta x\)) Count horizontal: RIGHT = (+). Always simplify fraction!
3. Guided Practice Models (Follow Along with Teacher)
MODEL 1: Positive Slope Going UP ↗
x y Run = +3 Rise = +4
Point A: ( , )
Point B: ( , )
Rise (\(\Delta y\)):
Run (\(\Delta x\)):
Slope \(m\): \(\frac{\text{\underline{\quad}}}{\text{\underline{\quad}}}\)
MODEL 2: Negative Slope Going DOWN ↘
x y Rise = -4 Run = +4
Point A: ( , )
Point B: ( , )
Rise (\(\Delta y\)):
Run (\(\Delta x\)):
Slope \(m\): \(\frac{\text{\underline{\quad}}}{\text{\underline{\quad}}} = \text{\underline{\quad}}\)
Slope Sleuth Guided Notes • Algebra 1 Page 1 of 2
SPECIAL CASES & SLEUTH PRACTICE
Student Name:
4. Special Cases: The "Zero" vs "Undefined" Breakdown
HORIZONTAL LINE
\(m = \frac{0}{\text{run}} = 0\)
Zero vertical rise! You can walk on flat ground without climbing or falling. Zero on TOP is OK!
VERTICAL LINE
\(m = \frac{\text{rise}}{0} = \text{UNDEFINED}\)
Zero horizontal run! In mathematics, dividing by zero is impossible. Zero on BOTTOM = NO WAY!
Sleuth Trap: Rise ALWAYS goes on top (\(\frac{\text{vertical}}{\text{horizontal}}\)). Never flip them!
Always reduce your final fractions!
5. Detective Challenge: Find the Slope (\(m\)) for Each Graph
Identify two points, find rise & run, then write \(m\)
Graph #1 Type: _________
Points: ( __ , __ ) & ( __ , __ )
Rise = ________ Run = ________
Slope \(m\) =
Graph #2 Type: _________
Points: ( __ , __ ) & ( __ , __ )
Rise = ________ Run = ________
Slope \(m\) =
Graph #3 Type: _________
Points: ( __ , __ ) & ( __ , __ )
Rise = ________ Run = ________
Slope \(m\) =
Graph #4 Type: _________
Points: ( __ , __ ) & ( __ , __ )
Rise = ________ Run = ________
Slope \(m\) =
6. Detective Debrief (Synthesis & Reflection)
1. If line \(A\) has a slope of \(m = 4\) and line \(B\) has a slope of \(m = \frac{1}{2}\), which line is steeper and why?
2. Why is the slope of any vertical line always undefined rather than zero?
Slope Sleuth Guided Notes • Algebra 1 Page 2 of 2
