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**Rebecca Fiorillo Camilla Jones Annie Gromelski**

Section 4.6: Slope Rebecca Fiorillo Camilla Jones Annie Gromelski

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**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-x x1-x2

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**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.

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**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.

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**Slope of Parallel and Perpendicular Lines**

m

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**Visual interpretations of slope**

Positive slope negative slope Zero slope no slope

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

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**Sample Problems Are these lines parallel?**

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

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**Sample Problems Are these lines parallel? C (2,10) A(2,6)**

mAB=6-2 =4 =2 = -2 mCD=10-4 =6 = 3 B(4,2) D(6,4) The lines are not parallel because they do not have the same slope.

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**Example Problems Given: D is the midpoint AC Find : 1. Slope of AC**

2. Slope of BD D F C(9,2)

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Answers -2/3 8/7

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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?

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

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**Example Problems Find slope of AC Find slope of AB C(6,6)**

3. Find slope of CB

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

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

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3.4 Find and use Slope of Lines. Slope Slope is: Rate of change A ratio of rise and run The change in Y over the change in X The m is Y = mX +b.

3.4 Find and use Slope of Lines. Slope Slope is: Rate of change A ratio of rise and run The change in Y over the change in X The m is Y = mX +b.

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