Download Forms of Linear Equations y m x

y
x=2
Forms of Linear Equations
x
st
All variables are to the 1 power
m=
y2 − y1
x2 − x1
Slope
y
1) Ax + By = C -or2) Ax + By + C = 0
Standard Form
A
m= −
B
y=3
x
To find the x-intercept (a, 0), let y = 0 and solve for x = a
To find the y-intercept (0, b), let x = 0 and solve for y = b
x=a
Vertical Line (not a function)
Undefined slope (vertical)
x-intercept (a,0) ex) x = 2 (top right), x-intercept ( 2,0)
No y-intercept when a ≠ 0
When a = 0, the line x = 0 is the y-axis
y =b
f ( x) = b
function notation
Horizontal Line
Slope is 0
y-intercept (0, b) ex) y = 3 (middle right) , y-intercept (0,3)
No x-intercept when b ≠ 0
When b = 0, the line y = 0 is the x-axis
y = mx + b
f ( x) = mx + b
function notation
Slope Intercept Form
Slope is m
y-intercept ( 0, b)
ex) y = x/2 + 2 (bottom right) m = ½, y-intercept (0, 2)
y − y1 = m( x − x1 )
Point-Slope Form
Slope is m
(
Line passes through x1 , y1
)
Parallel Lines have the same slope
m1 = m2 for parallel lines y = m1 x + b1 and y = m2 x + b2
ex) y = −3 x + 2 and y = −3 x − 4
Perpendicular Lines have slopes that are negative reciprocals
1
1
m1 = −
and m2 = −
for perpendicular lines y = m1 x + b1 and y = m2 x + b2
m2
m1
ex) y = −3 x + 2 and y = 13 x − 4
Page 1 of 1 line_equation_summary.DOC Ron Mower 9/4/02 6:20 AM
y = ½x + 2