Compare Lines with Different Slopes

3.2 Slope of a Line 1310 Fall 2011 Compare Lines with Different Slopes The slope (m) of a line indicates how quickly the y-value changes as x-value increases. Pick two distinct points (x1,y1) (x2,y2) on line y  y The slop formula m  2 1 computes the slope x2  x1 negative ` down left to right \ positive up left to right ⁄ zero horizontal __ undefined vertical | You may use either point as point 1 or point 2 (just not the same) If you are given the equation of the line, you can determine the slope by solving for y. y = mx + b The coefficient of x ( m ) is the value of the slope. Note: There are occasions when the value of x1 and x2 are the same (vertical line). In this case the slope is undefined (divide by 0 ) Determine if the graph increases or decreases [12] y = -4x + 2 [x1] -x + 2y = -6 [x2] x + y = x + 3 [x3] x + 3 = 4 Vertical and Horizontal Lines Vertical lines have a slope that is undefined. (Note: The x-values of any two points on a vertical line are equal - divide by zero ) Horizontal lines have a slope equal to zero. (Note: The y-values of any two points on a horizontal line are equal.) General Form of a Linear Equation Ax + By = C Example: 4x – y = 2 A = 4, B = -1, C = 2 Example: 3x + 2 = 2( 3x – 2 ) + 2x - 3y 3x + 2 = 6x - 4 + 2x - 3y 3x + 2 = 8x - 3y - 4 -8x + 3y -8x + 3y -5x + 3y + 2 = - 4 . - 2 - 2 -5x + 3y = - 6 A = -5, B = +3, C = -6 Graph Equations in Slope-Intercept Form Slope Intercept form: y = mx + b m is the slope b is the y-intercept ( 0, b ) Graph: [22] y = -2x + 3 Determine Slope and y-intercept, then graph [36] 5x + 3y = 6 Find the Slope-intercept Form Given Two Points on the Line y  y Compute the slope of the line using the slope formula m  2 1 x2  x1

Use either one of the points as (x1, y1) and the computed slope and put in x and y as the (x2, y2) point. Solve for y. Examples: Find the slope and y-intercept of the lines thru [44] ( 1, 7 ) and ( 3, 1 ) [50] ( 8, 2 ) and ( 8, -5 ) [52] ( -5, -1 ) and ( -3, -1 )