Linear Equation Notes

”Do not worry about your problems with mathematics, I assure you mine are far greater.” - Albert Einstein

Linear Equation Notes

Slope-Intercept Form: y = mx + b , where m = 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. Standard Form: Ax + By = C, where A, B, and C are constants. Point-Slope Form: y − y1 = m(x − x1 ) where m = slope and (x1 , y1 ) is a point on the line Definition of Slope: Given two points (x1 , y1 ) and (x2 , y2 ) on a line then y −y change of y ∆y m = x2 − x1 = = ∆x = rise run change of x 2 1 Horizontal Lines have 0 slope. Vertical Lines have an undefined slope. Parallel and Perpendicular Lines: Given two linear equations y1 = m1 x1 + b1 and y2 = m2 x2 + b2 , then If m1 = m2 then y1 k y2 (y1 is parallel y2 ) If m1 · m2 = −1 then y1 ⊥ y2 (y1 is perpendicular to y2 )

Created by: Matthew Westerhoff, 2006