2 What is slope? Slope equals Rise/Run. The slope of non-vertical line, segment, or ray containing (x1,y1) and (x2,y2) is defined by the formulam=y2-y1 or m=y1-y2x2-x x1-x2
3 What is slope? Continued Slope is used to find out or to describe the measurement of the steepness, incline, gradient, or grade of a straight line. Two points are used to find the slope with the y-points (rise)divided by the x-points (run).In other words, you are finding the ratio of the altitude change to the horizontal distance between any two points on the line.
4 Slope of Parallel and Perpendicular Lines Theorem 26: if two non-vertical lines are parallel, then their slopes are equal.Example: If RF ll AG and mRF =2/5 thenmAG=2/5Theorem 27: if the slopes of two non-vertical lines are equal, the lines are parallel.Example: if mCJ=3/7 and mMP=3/7, then the lines are parallel.
6 Visual interpretations of slope Positive slope negative slope Zero slope no slope
7 Sample ProblemsmAB=y2-y1 x2-x1 mAB= 5-(-3) 4-(-2) B (4,5) mAB= 8 = A (-2, -3)
8 Sample Problems Are these lines parallel? A (1,6) C (5,6) The Slopes are not parallel .mAB=6-1 = The lines are not oppositereciprocals due to thefact that CD is a horizontal linemCD=6-0 = which has no slope.D (5,0) B (8,1)
9 Sample Problems Are these lines parallel? C (2,10) A(2,6) mAB=6-2 =4 =2 = -2mCD=10-4 =6 = 3B(4,2) D(6,4)The lines are not parallel because they do not have the same slope.
10 Example Problems Given: D is the midpoint AC Find : 1. Slope of AC 2. Slope of BDD F C(9,2)