Linear Equations

A linear equation is an equation whose graph is a straight line.  Below are the various forms of linear equations.

ax + by = c

Standard Form

a, b, c are integers and both a and b can not equal zero.
x = k

Vertical Line

k is a real number and the x-intercept.  

This line has NO slope.
y = b

Horizontal Line

b is a real number and the y-intercept.  

This line has zero slope.
y = mx + b

Slope-Intercept Form

m is a real number and the slope of the line.

b is a real number and the y-intercept (where the line crosses the y-axis).
y = mx

m is the slope of the line.

This line intercepts the y-axis at the origin.
y - y1 = m(x - x1)

Point-Slope Form

m is the slope of the line

(x1, y1) is a point on the line.

slope =

m = (change in y) / (change in x)

= rise / run