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Course: Algebra I / Elementary Algebra
Topic: Lines and their Graphs
Subtopic: Slopes

Overview

Here we'll focus on the concept of slope which measures the steepness of a line. Slope is an important aspect of linear functions and has applications to real-life situations in the form of "rate" of growth. Some cautions to note:

• Watch your sign when you are finding slope! Anytime you move from point to point and you go down or left the sign will be negative on that side of the slope triangle.
• As you move from point to point, be sure to do just that in one smooth motion. Don't start at the right angle and move to one point, then start back at the right angle and move to the other point. If you do the signs may get messed up.
• When using the formula to find slope, it doesn't matter which point is (x1,y1) and which point is (x2,y2). But you do have to be careful that you don't mix the order up and use, say, y2-y1 on the top and x1-x2 on the bottom. If you do your signs will get messed up.
• Some textbooks say that vertical lines have "no slope". Don't confuse that with a "zero" slope! Horizontal lines have a slope of zero; vertical lines have "no slope" or better yet "undefined slope".

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 4.2.1 Given the graph of a line, find its slope
• 4.2.2 Given two points on a line, use the slope to find a third point on the line
• 4.2.3 Given two points on a line, find the slope of the line
• 4.2.4 Recognize lines that have positive slope, negative slope, zero slope, and undefined slope
• 4.2.5 Know that two parallel lines have the same slope
• 4.2.6 Know that two perpendicular lines have opposite reciprocal slopes
• 4.2.7 For horizontal and vertical lines know their equations, slopes, and axis-intercept points
• 4.2.8 Graph horizontal and vertical lines algebraically
• 4.2.9 Understand applications of slopes and rates

Terminology

Define: steepness, slope, slope triangle, rate of change (a.k.a. rate, rate of growth/decay), horizontal line, vertical line, zero slope, undefined slope

Slope Formula slope = rise / run = m = (y2-y1) / (x2-x1) (memorize it!)

Supplementary Resources

Read the two articles linked below. Both highly recommended!
Ask Dr Math's Why is the letter m used for slope?
and PurpleMath's The Meaning of Slope and Y-Intercept.