Lesson Description
In this lesson, students are introduced to slope as a measure of steepness on the coordinate plane. They will learn how to calculate slope using the formula “rise over run†and interpret whether a line has positive, negative, zero, or undefined slope.
Learning Objectives
- Define slope and explain what it represents.
- Calculate slope using rise over run.
- Determine slope from two points using a formula.
Topics Covered
- Rise and run
- Positive, negative, zero, and undefined slope
- Slope formula between two points
Key Terms
- Slope: A measure of how steep a line is, calculated as rise divided by run.
- Rise: The vertical change between two points.
- Run: The horizontal change between two points.
Lesson Examples
Example 1: Finding Slope from a Graph
- Choose two clear points on the line, such as (1,2) and (4,5).
- Calculate rise: 5 − 2 = 3.
- Calculate run: 4 − 1 = 3. Slope = 3/3 = 1.
Example 2: Using the Slope Formula
- Use the formula: m = (yâ‚‚ − yâ‚) / (xâ‚‚ − xâ‚).
- Substitute points (2,1) and (6,9).
- m = (9 − 1) / (6 − 2) = 8/4 = 2.
Practice Problems
- Find the slope between (0,0) and (3,6).
- Find the slope between (2,5) and (5,5).
- Find the slope between (4,1) and (4,7).
- Find the slope between (−1,3) and (2,9).
Tips & Common Mistakes
- Always subtract in the same order for numerator and denominator.
- If the run is zero, the slope is undefined.
- Horizontal lines always have slope zero.
Summary
Slope measures the steepness and direction of a line. It is calculated using rise over run or the slope formula. Positive slope rises left to right, negative slope falls left to right, zero slope is horizontal, and undefined slope is vertical.
Challenge Problems
- Find the slope between (−3,4) and (5,−2).
- Determine whether the points (1,2), (3,6), and (5,10) lie on the same line.
- A line rises 12 units for every 4 units it runs. What is the slope?