Rebecca Fiorillo Camilla Jones Annie Gromelski

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Objective - To find the slope of a line.

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Presentation transcript:

Rebecca Fiorillo Camilla Jones Annie Gromelski Section 4.6: Slope Rebecca Fiorillo Camilla Jones Annie Gromelski

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 formula m=y2-y1 or m=y1-y2 x2-x1 x1-x2

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.

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 then mAG=2/5 Theorem 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.

Slope of Parallel and Perpendicular Lines m

Visual interpretations of slope Positive slope negative slope Zero slope no slope

Sample Problems mAB=y2-y1 x2-x1 mAB= 5-(-3) 4-(-2) B (4,5) mAB= 8 = 4 6 3 A (-2, -3)

Sample Problems Are these lines parallel? A (1,6) C (5,6) The Slopes are not parallel . mAB=6-1 = 5 The lines are not opposite 1-8 -7 reciprocals due to the fact that CD is a horizontal line mCD=6-0 = 6 which has no slope. 5-5 0 D (5,0) B (8,1)

Sample Problems Are these lines parallel? C (2,10) A(2,6) mAB=6-2 =4 =2 = -2 2-4 -2 -1 mCD=10-4 =6 = 3 2-6 -4 -2 B(4,2) D(6,4) The lines are not parallel because they do not have the same slope.

Example Problems Given: D is the midpoint AC Find : 1. Slope of AC 2. Slope of BD D F C(9,2)

Answers -2/3 8/7

Example Problem 1.Given the points A=(3,5) and B=(4,9). Find the slope of line AB. 2. What is the slope of a horizontal line?

Answers mAB= 4 The slope of a horizontal line is 0.

Example Problems Find slope of AC Find slope of AB C(6,6) 3. Find slope of CB

Answers mAC = 5 mAB = 3/-2 mCB = -8

Works Cited "Math Facts.info: Slope." Math Facts.info: Mathfacts. Web. 19 Jan. 2011. <http://mathfacts.info/slope.html>.