1. MTH 070 Elementary Algebra
Chapter 3
Linear Equations, Slope, Inequalities,
and Introduction to Functions
Section 3.4
Determining the Equation
of a Line, Parallel Lines,
and Perpendicular Lines
Copyright © 2010 by Ron Wallace, all rights reserved.

2. Linear Equations in Two Variables – Where we’ve been…
Two Forms
Standard form: Ax + By = C
x-intercept: (C/A,0)
y-intercept: (0,C/B)
Slope-Intercept from: y = mx + b
slope:
y-intercept: (0,b)
Graph
Two points need
Picture of ALL ordered pairs/solutions

3. Finding the Equation
Often we know information about a line and need to determine its equation.
Possible sufficient information
5 options ……….?

4. Finding the Equation
Often we know information about a line and need to determine its equation.
Possible sufficient information
Two Points (most common in applications)
A Point and the Slope
The y-intercept & the Slope
Both intercepts (not origin)
Graph

5. Finding the Equation Two Points (most common in applications)
Calculate the slope
Use the slope and either point to determine the equation (next option)
Example: (2,3) & (–5,7)

6. Finding the Equation A Point and the Slope Example: (2,3) & m = –4/7
Use the slope formula with (x,y) as one point and the given point as the other point.
Example: (2,3) & m = –4/7

7. Most general method – works in all situations!
Finding the Equation
Point-Slope Forms
Most general method – works in all situations!

8. Finding the Equation The y-intercept & the Slope
Use the slope-intercept form
y = mx + b
m = slope
b = y-intercept
Example: (0,9) & m = 3

9. Finding the Equation Both intercepts (not origin) Method 1
Special case of two points: (a,0) & (0,b)
Method 1
Calculate m = –b/a & use y = mx + b
Example: (2,0) & (0,–5)

10. Finding the Equation Both intercepts (not origin) Method 1 Method 2
Special case of two points: (a,0) & (0,b)
Method 1
Calculate m = –b/a & use y = mx + b
Method 2
Write intercepts as fractions with the same numerator: (C/A,0) & (0, C/B)
Use standard form: Ax + By = C
Example: (2,0) & (0,–5)

11. Finding the Equation Graph Example:
By observation, determine two points or one point and the slope (rise/run)
Note: If possible, use the y-intercept
Example:

12. Finding the Equation
Horizontal Lines
Example:

13. Finding the Equation
Vertical Lines
Example:

14. Finding the Equation Parallel Lines Examples
What is true about parallel lines?
Same slope
Examples
Find the equation through (0,3) that is parallel to y = 2x + 5
Find the equation through (2,3) that is parallel to y = 2x + 5

15. Finding the Equation Perpendicular Lines
What is true about perpendicular lines?
Slopes have opposite signs
m2 = –1/m1

16. Slopes of Perpendicular Lines
90 c
Slope of Red Line = b 
Slope of Blue Line = c

17. Finding the Equation Perpendicular Lines Examples
What is true about perpendicular lines?
m2 = –1/m1
Examples
Find the equation through (0,3) that is perpendicular to y = 2x + 5
Find the equation through (2,3) that is perpendicular to y = 2x + 5