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

3. IN LAYMAN’S TERMS:

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

5. 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?

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

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

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

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

10. Use the following endpoints to calculate slope with the given formula. Could these lines be wheelchair ramps? Practice Problems: 1. (4,6) (-2,3) 2. (5,-7) (6,7) 3. (3,-2) (4,3)

11. NOW TRY THESE ON YOUR OWN Find the slope of a line that contains each pair of points: 1.R(9, -2) S(3, -5) 2.M(7, -4) N(9, 4)

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

13. 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? 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?

14. 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). 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 Therefore 92.4 = Y – 1074.4 2010 – 2000 2010 – 2000 92.4 = Y - 1074.4 92.4 = Y - 1074.4 10 10 924 = Y – 1074.4 924 = Y – 1074.4 1998.4 = Y 1998.4 = Y Therefore the total sales would be projected to be Therefore the total sales would be projected to be $1998.4 million. $1998.4 million.

15. 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

16. Horizontal lines have a slope of zero while vertical lines have no slope HorizontalVertical m = 0 m = no slope

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

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

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

20. Answers Neither Neither Parallel Parallel

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

22. TWO LINES MAY HAVE THE SAME SLOPE

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

24. 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