Section 4.6: SlopeRebecca FiorilloCamilla JonesAnnie 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 slopePositive slope negative slope

Zero slope no slope

Sample ProblemsmAB=y2-y1 x2-x1

mAB= 5-(-3) 4-(-2) B (4,5)

mAB= 8 = 4 6 3

A (-2, -3)

Sample ProblemsAre 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 ProblemsAre 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 ProblemsGiven: D is the midpoint AC B( 13,12)

Find : 1. Slope of AC A (3,6)

2. Slope of BD D F

C(9,2)

Answers1. -2/32. 8/7

Example Problem1.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?

Answers1. mAB= 42. The slope of a horizontal line is 0.

Example Problems1. Find slope of AC2. Find slope of AB C(6,6)

A(4,-4) B(8,-

10)

3. Find slope of CB

Answers1. mAC = 52. mAB = 3/-23. mCB = -8

Works Cited"Math Facts.info: Slope." Math Facts.info: Mathfacts. Web. 19 Jan. 2011.

<http://mathfacts.info/slope.html>.