linear equation notes

Definition of Slope:Given two points (x1, y1) and (x2, y2) on a line then

m =y2 − y1x2 − x1

=change of ychange of x

=∆y∆x = rise

run

Horizontal Lines have 0 slope.Vertical Lines have an undefined slope.

Parallel and Perpendicular Lines:Given two linear equations y1 = m1x1 + b1 and y2 = m2x2 + b2, then

If m1 = m2 then y1 ‖ y2 (y1 is parallel y2)

If m1 ·m2 = −1 then y1 ⊥ y2 (y1 is perpendicular to y2)

Point-Slope Form:y − y1 = m(x− x1) wherem = slope and (x1, y1) is a point on the line

Standard Form:Ax + By = C, whereA, B, and C are constants.

Slope-Intercept Form:y = mx + b , wherem = slope and b = ordinate of the y-intercept.x is the independent variable and y is the dependent variable.

To find x-intercept let y = 0 and solve for x.To find y-intercept let x = 0 and solve for y.

Linear Equation Notes Created by: Matthew Westerhoff, 2006”Do not worry about your problems with mathematics,I assure you mine are far greater.” - Albert Einstein

1