Forms of the Line
y = kx
Not really a form of the line, but a special case.
k is the constant of variation.
Point-Slope Form
Most useful to write the equation when given a point and a slope.
m is the slope.
x1 and y1 come from a point on the line. (x1, y1)
Slope-Intercept Form
y = mx + b
Most useful for graphing lines, or when given information about the graph.
m is the slope.
b is the y-coordinate of the y-intercept. (0, b)
Standard Form
Ax + By = C
Designed so that everyone writes the equation in a "standard" way. Sometimes useful when using the "Graph by Intercepts" method.
A, B, and C should be integers if possible. (No decimals or fractions.)
A cannot be negative.
B cannot be negative if A is 0. B cannot have any common factors with A.
C cannot have any common factors with A or B.
Bonus Forms of the Line
(Not usually used in 8th grade)
Point-Point Form
Most useful to write the equation when given two points
x1 and y1 come from a point on the line. (x1, y1)
x2 and y2 come from another point on the line. (x2, y2)
Intercept Form
Most useful to write the equation when given the x and y intercepts.
a is the x-coordinate of the x-intercept. (a, 0)
b is the y-coordinate of the y-intercept. (0, b)
