2What 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
3What 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.
4Slope 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.
6Visual interpretations of slope Positive slope negative slope Zero slope no slope
7Sample ProblemsmAB=y2-y1 x2-x1 mAB= 5-(-3) 4-(-2) B (4,5) mAB= 8 = A (-2, -3)
8Sample 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)
9Sample 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.
10Example Problems Given: D is the midpoint AC Find : 1. Slope of AC 2. Slope of BDD F C(9,2)