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

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

5. Slope of Parallel and Perpendicular Lines m

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

7. Sample Problems
mAB=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 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)

9. 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.

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

11. Answers
-2/3
8/7

12. 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?

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

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

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

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