This document discusses linear equations in the form y=mx+b. It defines slope as rise over run, and the y-intercept as the point where the line crosses the y-axis. It provides examples of special lines with undefined or zero slopes. It explains how to find the equation of a line given two points, given slope and a point, or given just the slope and y-intercept. It also notes how to graph lines by starting at the y-intercept and moving up the rise and over the run.

1. February 6, 2008 Linear Equations y = mx + b

2. Slope = rise = m = run difference of y’s difference of x’s (3, 2) (4, 7) 7 – 2 = 5 = 5 4 – 3 1

3. y – intercept = b = the point where the line crosses the y axis = starting point when graphing b = -6

4. Special lines only contain one variable: x = any number ( vertical line ) Slope: Undefined x = 7 y = any number ( horizontal line ) Slope : Zero y = 7

5. Finding the equation of the line in y= mx + b form. Given: Two points. First find the slope (m) and then substitute one of the points x and y values into point-slope form (y – y 1 = m(x – x 1 ) along with the slope. Simplify.

6. Finding the equation of the line in y = mx + b form. Given: slope (m) and a point (x,y). Substitute x, y, and m into point-slope form and simplify. (y – y 1 = m(x – x 1 )

7. Finding the equation of the line in y= mx + b form. Given: slope and y-intercept. Substitute the “m” with the slope value and the “b” with the y-intercept value. Slope: 5 y-intercept: -2 Equation: y = 5x - 2

8. Graphing the line – start with the y-intercept and then move the rise and then the run. Positive slopes increase from left to right. Negative slopes decrease from left to right