 General Concepts About Linear Equations
 A linear equation is the equation of a line.
 The graph of a line is a graphical view of the set of all points that make
the equation true (in other words, all points that work in the equation or
all points that satisfy the equation).
 Forms of Equations of Lines
 a, b, c, and m are real numbers
Form 
Equation 
Note 
Standard 
ax + by = c

a and b are not both 0.

SlopeIntercept 
y = mx + b

m is the slope of the line.
(0, b) is the yintercept.
(discussed in Section 3.3)

PointSlope 
y  y_{1} = m(x  x_{1})

(x_{1}, y_{1}) is a particular point on the line.
m is the slope of the line.
(discussed in Section 3.3)

 xintercept
The xintercept is the point where the graph crosses the xaxis.
The ycoordinate of the xintercept is 0.
To find the xintercept:
 Set y = 0 in the equation.
 Solve for x. The value obtained is the xcoordinate of the xintercept.
 The xintercept is the point (x, 0), with x the value found in step 2.
 yintercept
The yintercept is the point where the graph crosses the yaxis.
The xcoordinate of the yintercept is 0.
To find the yintercept:
 Set x = 0 in the equation.
 Solve for y. The value obtained is the ycoordinate of the yintercept.
 The yintercept is the point (0, y), with y the value found in step 2.
 Graphing Lines by Plotting Points
 The idea:
 Find two points on the line.
 Plot the two points.
 Draw a straight line between the two points.
 Finding two points on the line:
 Pick a value for x (or y).
 Solve for y (or x, if you picked a value for y).
 The point (x, y) is a point on the line.
 Repeat steps 1  3 for a different value of x (or y).
 An easy choice is to find the xintercept (by setting y = 0 and solving for x).
 Another easy choice is to find the yintercept (by setting x = 0 and solving for y).
 Vertical Lines
Equations of the form x = a are vertical lines.
The xcoordinate of every point on the vertical line x = a has the value "a".
 Horizontal Lines
Equations of the form y = a are horizontal lines.
The ycoordinate of every point on the horizontal line y = a has the value "a".
