SLOPE

1. SLOPE The ratio of the vertical change to the horizontal change

2. IN LAYMAN’S TERMS: Slope is the measure of the steepness of a line!

3. Wheelchair Ramps • Ramp steepness is governed by the American’s with Disabilities ACT. • ADA Accessibility Guidelines for Buildings and Facilities (ADAAG) are located at: http://www.access-board.gov/adaag/html/adaag.htm#4.8 How steep of a ramp should be acceptable for a person in a wheelchair?

4. Stairs are an excellent example of slope Most of us are familiar with associating ‘stairs’ with ‘slope’. Do you have any questions about finding the slope of stairs? You can place a board over any set of stairs and get a ramp, but would the slope always be acceptable for strollers and wheelchairs?

5. HOW IT’S FIGURED: VERTICAL CHANGE ___________________ STEEPNESS = HORIZONTAL CHANGE **OR** Change in Y-axis ___________________ SLOPE (m) = Change in X-axis

6. Using the Slope Formula when given 2 endpoints This is an X Lets make it our 1st X This is a Y. Lets make it our 1st Y Another X. It’s our 2nd one. Another Y. Its our 2nd one. Lets plug it in and solve for slope (m).

7. WORK TIME! Find the slope of a line that contains points A(-2, 5) B(4, -5)

8. HERE’S HOW YOU SOLVE IT: Change in Y-axis ___________________ SLOPE (m) = Change in X-axis 5 – (-5) ___________________ m of line AB = -2 - 4 10 ___________________ = -6 5 ___________ - = 3

9. Use the following endpoints to calculate slope with the given formula. Could these lines be wheelchair ramps? Practice Problems: • (4,6) (-2,3) • (5,-7) (6,7) • (3,-2) (4,3)

10. NOW TRY THESE ON YOUR OWN Find the slope of a line that contains each pair of points: • R(9, -2) S(3, -5) • M(7, -4) N(9, 4)

11. Slope • Slope is also known as a “rate of change”. • Rate of change describes how a quantity changes over time.

12. Example • Between 1990 and 2000, annual sales of electronic games equipment increased by an average rate of 92.4 million per year. In 2000, the total sales were $1074.4 million. If sales increase at the same rate, what will the total sales be in the year 2010?

13. Answer: • Let our first (x,y) be (2000, 1074.40), which represents (time, value). The rate of change (slope) would be 92.4, and our second (x,y) would be (2010, Y). • Therefore 92.4 = Y – 1074.4 • 2010 – 2000 • 92.4 = Y - 1074.4 • 10 • 924 = Y – 1074.4 • 1998.4 = Y • Therefore the total sales would be projected to be • $1998.4 million.

14. If a line goes up from left to right, then the slope has to e positive Conversely, if a line goes down from left to right, then the slope has to be negative

15. Horizontal lines have a slope of zero while vertical lines have no slope m = 0 Vertical Horizontal m = no slope

16. Parallel Lines have the same slope. • Postulate: • Two nonvertical lines have the same slope if and only if they are parallel.

17. Perpendicular lines have opposite reciprocal slopes. • Postulate: • Two non-vertical lines are perpendicular if and only if the product of their • slopes is -1.

18. Example • Determine whether line FG and line HJ are perpendicular, parallel or neither. • F (1,-3) G(-2,-1) H(5,0) J(6,3) • F(4,2), G(6,-3) H(-1,5) J(-3,10)

19. Answers • Neither • Parallel

20. True or False?? ALL HORIZONTAL LINES HAVE THE SAME SLOPE

21. TWO LINES MAY HAVE THE SAME SLOPE

22. A LINE WITH A SLOPE OF 1 PASSES THROUGH THE ORIGIN

23. THE ANSWERS! #1: All horizontal lines have the same slope. TRUE #2: Two lines may have the same slope. TRUE #3: A line with a slope of 1 passes through the origin. FALSE