MTH 070 Elementary Algebra Section 3.3 The Slope and y-Intercept Method Chapter 3 Linear Equations, Slope, Inequalities, and Introduction to Functions Copyright © 2010 by Ron Wallace, all rights reserved.

A quick review … Ax + By = C is a linear equation (L.E.) Alternate form: y = mx + b Standard from  Alternate form 2 points will determine a line Solutions of a L.E. are ordered pairs (x,y) All solutions of a L.E. form a line. All points on a line will satisfy a L.E. 1 of 2

A quick review … Intercepts, from standard form Ax + By = C x-intercept: (C/A, 0) y-intercept: (0, C/B) Graphing a L.E. … Determine 2 or 3 solutions; plot; draw line Determine intercepts; plot; draw line 2 of 2

Slope The steepness of a line left to right up hill = + down hill = – flat (i.e. horizontal) = 0 given two points ( x 1,y 1 ) & ( x 2, y 2 ) …

Slope – Examples

The alternate form y = mx + b Find the y-intercept … y = m(0) + b y = 0 + b y = b y-int: (0, b) !

The alternate form y = mx + b Find the slope … First Point (y-intercept): (0, b) Let x = 1 … y = m(1) + b = m + b Second Point: (1, m+b) Slope = = m !

The alternate form y = mx + b Therefore … y-intercept: (0, b) Slope: m y = mx + b is called the slope-intercept form of a line.

Using the y-intercept and slope to graph a line. Plot the y-intercept: (0, b) View the slope as a fraction. m = rise/run (if negative, put the – with the rise) From the y-intercept, move up or down the distance given by the rise. positive rise  up negative rise  down From there, move to the right the distance given by the run … giving a second point. Use the two points to draw the line.

Using the y-intercept and slope to graph a line. Examples