Slope of intercept for grade 8 students.pptx

this is a lesson for slope

1. L earning Competencies illustrates and finds the slope of a line given two points, equation, and graph writes the linear equation ax + by = c to in the form y = mx + b and vice versa graphs a linear equation given (a) any two points; (b) x – and y – intercepts; (c) the slope and a point on the line describes the graph of a linear equation in terms of its intercepts and slope finds the equation of a line (a) two points; (b) the slope and a point; (c) the slope and its intercepts

2. Slope The slope of a line is a measure of the steepness of the line. Given two points on a line, the slope is the ratio of the vertical change or rise between the points and the horizontal change or run between the points. The symbol for slope is m . 𝑚 = rise run

3. Slope Formula The slope of a line containing two points (𝑥 1 , 𝑦 1 ) , is given by 𝑦 − 𝑦 2 1 𝑥 2 − 𝑥 1 ; 𝑥 1 ≠ 𝑥 2 Slope = m =

4. Example 1: Find the slope of the line containing the points (2,5) and (-3,7). Solution:

5. Example 1: Find the slope of the line containing the points (2,5) and (-3,7). Solution: Let (2,5) be (𝑥 1 , 𝑦 1 ) and (-3,7) be (𝑥 2 , 𝑦 2 ), then by definition of slope, 𝑚 = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 −( ) = 7−5 = = −( ) −3−2 2 = −2 −5 5

6. Example 2: Find the slope of the line containing the points (5,8) and (2,3). Solution:

7. Example 2: Find the slope of the line containing the points (5,8) and (2,3). Solution: Let (5,8) be (𝑥 1 , 𝑦 1 ) and (2,3) be (𝑥 2 , 𝑦 2 ), then by definition of slope, 𝑚 = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 = −( ) = 3−8 − ( ) 2 − 5 = −5 = 5 −3 3

8. Example 3: Find the slope of the line containing the points (3,4) and (-2,4). Solution:

9. Example 3: Find the slope of the line containing the points (3,4) and (-2,4). Solution: Let (3,4) be (𝑥 1 , 𝑦 1 ) and (-2,4) be (𝑥 2 , 𝑦 2 ), then by definition of slope, 𝑚 = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 −( ) = 4−4 − ( ) − 2 − 3 = = − 5 =

10. Example 4: Find the slope of the line containing the points (-5,8) and (-5,3). Solution:

11. Example 4 : Find the slope of the line containing the points (-5,8) and (-5,3). Solution: Let (-5,8) be (𝑥 1 , 𝑦 1 ) and (-5,3) be (𝑥 2 , 𝑦 2 ), then by definition of slope, 𝑚 = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 = −( ) = 3−8 − ( ) − 5 − ( − 5 ) = −5 = undefined

12.   Equation of a Line

13. that passes through the points:   Equation of a Line

14. (2, 5) and (-3, 7) (5, 8) and (2, 3) (3, 4) and (-2, 4) (-5, 8) and (-5, 3) Equation of a Line