Expanded Syllabus
Chapter 2 : The Rectangular Coordinate System and Graphs of Equations

(x, y)

College Algebra 
by Examples

Chapter Summary
MathGV - Graphing Program


2.1 The Rectangular Coordinate System

Points: P(x1 , y1) and Q(x2 , y2), where x1 is the x-coordinates with the smallest value 

Distance between P and Q is given by d:

Midpoint between P and Q is given by the coordinates:

Equation of Vertical line is x = a
Equation of Horizontal line is y = a

2.2 Slope of a Nonvertical Line
 
 

Slope of a line is given by formula

For points: P(x1 , y1) and Q(x2 , y2)

For 2 lines with slopes  :

Slope  if line is a horizontal line

Slope  is undefined if line is a vertical line

Slope  if both lines are parallel

Slope  if lines are perpendicular

2.3 Writing Equations of Lines

General form: 

Point-Slope form: 

Slope-intercept form: 

2.4 Graphs of Equations

Intercepts:

(a) y-intercept: value of y when x = 0

(b) x-intercept(s); values of x when y = 0

Symmetry:

(a) About the y-axis if 

(b) About the origin is 

Equation of a Circle:

(a)  , where center is (0, 0)

(b)  , where center is (h, k)

2.5 Proportion and Variation

Directly Proportional, k is constant of proportionality 

Inversely Proportional:

Joint Proportional:

Combine