Intermediate Algebra – Student Workbook – Second Edition 2013

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Date: ________________
Mini-Lesson 1b
The topic of linear equations should be at least slightly familiar to students starting Intermediate
Algebra. The basics are covered here with reminders of important ideas and concepts that will be
heavily utilized in the next lesson.
What is a Linear Equation?
A LINEAR EQUATION is an equation that can be written in the form:
y = mx + b
with slope, m, and y-intercept (0, b)
This is the SLOPE-INTERCEPT form for the equation of a line.
Slope
The slope of a line is denoted by the letter m. Given any two points, (x 1 , y 1 ), (x 2 , y 2 ), on a line,
the slope is determined by computing the following ratio:
y2
y1
m
x x
Note: Slope is also referred to as the “change in y” over the “change in x” and is a measure of
steepness and direction for a given line.
2
1
Problem 1 WORKED EXAMPLE – DETERMINE SLOPE OF A LINEAR EQUATION
Find the slope of the line through Find the slope of the line through
the points (2, -5) and (-3, 4). the points (-2, -4) and (4, 8)
4 ( 5)
m
3 (2)
4 5
5
9
5
9
5
8 ( 4)
m
4 ( 2)
8
4
12
6
2
4
2
Note: The slope is negative indicating the line decreases from left to right. If slope is positive,
then the line increases from left to right.
Scottsdale Community College Page 29 Intermediate Algebra