1. Slope
Chapter 8
Section 8.3

2. Objective
Students will find the slope of a line

3. Concept
You can describe the steepness, or slope, of a path by giving the ratio of its vertical rise to its horizontal run. rise to run rise run

4. Concept
To describe the slope of a straight line, first choose any two points on the line. Then count the units in the rise and the units in the run from one point to the other. The ratio of the rise to the run is the slope of the line.

5. Example

6. Example

7. Concept
The first two examples show line that have a positive slope. Lines that rise more steeply as you move from left to right have a greater slope. The next two examples show lines that fall as you move from left to right. The rise of these lines is negative, and so is their slope.

8. Concept

9. Concept

10. Concept
The slope of a line can be defined by using the coordinates of a pair of points on the line. Slope (m) = rise = vertical change = difference of y run horizontal change difference of x

11. Concept
Suppose that (x1, y1), reads “x sub 1, y sub 1” (x2, y2), reads “x sub 2, y sub 2” are any two different points on a line. We have the following slope formula

12. Concept
Slope (m) = y2 – y1 x2 – x1

13. Concept
When you find the slope of a line, the order in which you consider the points is not important. However, you must use the same order for finding both the difference between the y-coordinates and the difference between the x-coordinates. If you don’t, the result will be the opposite of the slope.

14. Find the slope of a line through the points (-2, 3) and (4, 8)
Example
Find the slope of a line through the points (-2, 3) and (4, 8)

15. Find the slope of the line through the points (1, 2) and (-3, -4)
Example
Find the slope of the line through the points (1, 2) and (-3, -4)

16. Find the slope of the line through the points (7, -6) and (-5, 2)
Example
Find the slope of the line through the points (7, -6) and (-5, 2)

17. Find the slope of the line with equation 2x + 4y = 12
Example
Find the slope of the line with equation 2x + 4y = 12

18. Find the slope of each line a. y = 3 b. x = 4
Example
Find the slope of each line a. y = 3 b. x = 4

19. The slope of every horizontal line is 0 A vertical line has no slope
Concept
The slope of every horizontal line is 0 A vertical line has no slope

20. Questions

21. Assignment
Worksheet