The document discusses how to calculate the slope of a line given two points on the line. It provides two methods: 1) The slope formula, which is the rise over the run between two points (change in y over change in x). 2) The algebraic method, where the slope m is calculated as (y2 - y1) / (x2 - x1). It also notes that horizontal lines have a slope of 0, and vertical lines have undefined slopes.

1. Objective- To find the slope of a line given two points. Graph y = 2x - 3 x y -3 -2 -1 0 1 2 3 -9 -7 -5 -3 -1 1 3 x y y = 2x - 3

2. Objective- To find the slope of a line given two points. x y y = 2x - 3 Slope of a line Slope (m) = vertical change horizontal change Slope (m) rise run Slope (m) = = y x Slope (m) = + 2 + 1 + 2 + 1 m = 2 - 2 - 4 - 4 - 2 = y-intercept = -3

3. Find the slope of the line below. x y Slope (m) rise run = + 1 + 3 Slope (m) = + 1 + 3 m = 1 3

4. Find the slope of the line below. x y Slope (m) rise run = + 3 + 2 Slope (m) = + 3 + 2 m = 3 2

5. Find the slope of the line below. x y Slope (m) rise run = - 1 + 4 Slope (m) = - 1 + 4 m = - 1 4

6. Find the slope of the line below. x y Slope (m) rise run = - 4 + 2 Slope (m) = - 4 + 2 m = - 2

7. Find the slope of the line below. x y Slope (m) rise run = + 2 + 5 Slope (m) = + 2 + 5 m = 2 5

8. Find the slope of the line below. x y Slope (m) rise run = - 4 + 1 Slope (m) = - 4 + 1 m = - 4

9. Algebraic Method to Find Slope Given Two Points y Slope (m) rise run = Slope (m) y x Slope (m) = = (1,2) ( - 2, - 3) y 2 - y 1 x 2 - x 1 2 1 Slope (m) = 2 - - 3 1 - - 2 Slope (m) = 5 3 m = 5 3

10. Algebraic Method to Find Slope Given Two Points Slope (m) = y 2 - y 1 x 2 - x 1 m = 7 - 3 4 - - 1 m = 4 5 m = 4 5 Find the slope between (-1,3) and (4,7). 1 2

11. Algebraic Method to Find Slope Given Two Points m = y 2 - y 1 x 2 - x 1 m = 7 - 5 - 1 - 6 m = 2 - 7 m = - 2 7 Find the slope between (6,5) and (-1,7). 1 2

12. Algebraic Method to Find Slope Given Two Points m = y 2 - y 1 x 2 - x 1 m = 7 - 1 - 8 - 4 m = 6 - 12 m = - 1 2 Find the slope between (-8,7) and (4,1). 2 1

13. Slope of Horizontal and Vertical Lines y x y x Horizontal Lines Vertical lines y = 2 y = 2 x = - 3 x = - 3 m = 0 m = undefined

14. Slope of Horizontal and Vertical Lines y x y x x = - 3 (-2,2) (1,2) (-2,2) (1,2) (-3,2) (-3,-1) (-3,2) (-3, -1) Horizontal Lines Vertical lines y = 2

15. Slope of Horizontal and Vertical Lines m = y 2 - y 1 x 2 - x 1 1 2 m = 2 - 2 1 - - 2 m = 0 3 m = 0 m = 0 for all Horizontal Lines m = y 2 - y 1 x 2 - x 1 1 2 m = - 1 - 2 - 3 - - 3 m = - 3 0 m = undefined or there is “no slope” m = undefined for all Vertical Lines Watch Out! (-2,2) (1,2) (-3,2) (-3, -1) Horizontal Lines Vertical lines