1. Wed, 12/7 SWBAT…compute slope
Agenda
WU (10 min)
Notes on slope (35 min)
Warm-Up: 1.
HW#3: Slopes of lines (front & back) 1

2. How do engineers build bridges?

4. How do engineers build roads?

6. How do builders build roofs?

8. How can we write 7% as a fraction?

9. 7% as a fraction??
Remember than any percent is a part of 100.

10. The grade or incline of a road is the same as slope
Here is the picture:
7 feet
100 feet

11. Slope of a line (m) To find the slope, use the formula (elevacion)4
(elevacion)
(desplazamiento) 4

12. Slope of a line (m)
To find the slope, use the formula 4 4

13. Slope of a line (m) Find the slope of the following lines: A) B) 2 2 13

14. Why do we use m for slope?
Possibly because m comes from the French word “monter”, which means to climb
The earliest textbooks used m, and everyone else just copied it

15. Slope of a line (m) Is the slope positive or negative? Answer:
Positive, read from left to right

16. Try for yourself
Using the graph paper squares, draw lines with the following slopes.
Start anywhere on your coordinate plane.
A) B)
Label your lines with their slopes
Glue the graphs in your note book

19. Slope of a line (m)
The last 2 lines had a positive slope, let’s look at slopes with negative slopes

20. Slope of a line (m)
We still use rise over run, except the “stairs” are underneath the line. -2 3

21. Try for yourself
Using the graph paper squares, draw lines with the following slopes.
Start anywhere on your coordinate plane.
C) D)
Glue the graphs in your note book

24. Your turn
Slope = 2/4 = 1/2

25. “Official” Definition of Slope
Slope is the change in the vertical distance (rise) over the change in the horizontal distance (run)
Pendiente: Razon del cambio en la coordenada y (elevacion) al cambio correspondiente en la coordenada x (desplazamiento) a medida que uno se mueve de un punto a otra en una recta.

26. Question
Find the slope of the line that passes through (1, 0) and (-1, -1).
(x1, y1)
(x2, y2)
(To see the slope visually… Plot these points. Connect the line (don’t forget arrows)).
m = (y2 – y1)/(x2 – x1)
= (-1 – 0)/(-1 – 1))
= -1/-2
m = 1/2

27. What the graph looks like1 2 m =

28. Find the rate of change:x y 2 1 4 6 -1
m = (y2 – y1)/(x2 – x1)
= (2 – 1) / (0 – 2)
= 1/-2
= -1/2

29. Directions: Find the value of r so the line that passes through each pair of points has the given slope.
(12, 10), (-2, r) m = -4
r = 66

30. Horizontal lines have a slope of ___ Vertical lines have a slope of ___
m = 0
Vertical
Horizontal
m = undefined

31. Practice Problem
A horizontal lines passes through (2, 5). What other point does the line contain?
(2,3)
(0,5)
(5,10)
(0,2)