Grade 8 Mathematics Q2 w1
- 2. Most Essential Learning Competencies differentiates linear inequalities in two variables from linear equations in two variables. Illustrates and graphs linear inequalities in two variables. solves problems involving linear inequalities in two variables.
- 3. A linear inequality is almost the same as a linear equation, except the equals sign is replaced with an inequality symbol. It can be written in different forms such as:
- 4. Linear Inequality “ax + by is less than c” “ax + by is greater than c” “ax + by is less than or equal to c” “ax + by is greater than or equal to c” ax + by ≤ c ax + by ≥ c ax + by < c ax + by > c
- 5. Example 1: x-y < 5
- 6. Example 2: 5x+4y > 20
- 7. Example 3: 2x+3y ≤ 6
- 8. Example 4: x – y ≥ 7
- 10. Differentiate Linear equations and Linear Inequality
- 12. Example of Linear EQUATION 1. 2x + 5y = 10 As you can see it forms a line
- 13. Example of Linear EQUATION 2. 3x -4y =12 Again this example forms a line
- 14. Example of Linear INEQUALITY 1. 3x – y ≤ 9 It has a shaded region and a solid line as a boundary.
- 15. Example of Linear INEQUALITY 2. 2x - 3y > 60 It has a shaded region and a solid line as a boundary.
- 16. Assessment Card
- 17. Graphs Linear Inequalities in Two Variables
- 18. The Graph of a Linear Inequality is the set of all points that are solutions to the inequality. Step 2: Solve for the boundary line of the graph using x and y intercept method. Let y = 0 Let x = 0 x + y = 4 x + y = 4 x + 0 = 4 0 + y = 4 x = 4 y = 4 (4 ,0) (0,4) Points (4,0) and (0,4) will be the boundaries of the graph. 2 Step 1: Change the inequality x + y < 4 into an equation x + y = 4. 1 Example 1: x + y < 4
- 19. The Graph of a Linear Inequality
- 20. The Graph of a Linear Inequality Step 4: Decide which part of the plane will be shaded by performing test point (0,0) to the inequality. Substitute x = 0 and y= 0 to x + y < 4 x + y < 4 0 + 0 < 4 0 < 4 - TRUE If proven TRUE, the half plane that contains the origin will be shaded and if it is FALSE, the origin must not be included in shading. 4 Step 3: Determine what type of line (solid or broken) will be used. For symbols > or < use broken lines. Therefore. the two points on the boundary line (4,0) and (0,4) will be holes. 3
- 21. The Graph of a Linear Inequality Step 5: Since 0 < 4 is TRUE, the graph will be: The origin (0,0) is included. The shaded region contains all the possible solutions to the inequality x + y < 4. 5
- 22. The Graph of a Linear Inequality Step 2: Solve for the boundary line of the graph using x and y intercept method. Let y = 0 Let x = 0 8x – 6y = 24 8x – 6y = 24 8x – 6(0) = 24 8(0) - 6 y = 24 8x – 0 = 24 0 - 6y = 24 8x = 24 -6y = 24 x = 3 y = -4 (3,0) (0,-4) Points (3,0) and (0,-4) will be the boundaries of the graph. 2 Step 1: Change the inequality 8x – 6y ≥ 24 into equation 8x – 6y = 24. 1 Example 2: 8x – 6y ≥ 24
- 23. The Graph of a Linear Inequality
- 24. The Graph of a Linear Inequality Step 4: Decide which part of the plane will be shaded by performing test point (0,0) to the inequality. Substitute x = 0 and y= 0 to 8x – 6y ≥ 24 8(0) – 6(0) ≥ 24 0 - 0 ≥ 24 0 ≥ 24 – FALSE If proven TRUE, the half-plane that contains the origin will be shaded and if it is FALSE, the origin must not be included in shading. 4 Step 3: Determine what type of line (solid or broken) will be used. For symbols ≥ or ≤ use a solid line. Therefore the two points on the boundary line (4,0) and (0,4) will be part of the line. 3
- 25. The Graph of a Linear Inequality Step 5: Since 0 ≥ 24 is FALSE, the graph will be: The origin (0,0) is not included. The shaded region contains all the possible solutions for the given inequality 5
- 26. Assessment Card
- 27. A Picture Always Reinforces the Concept Images reveal large amounts of data, so remember: use an image instead of long texts
- 28. THANK YOU! Excited to be BTS! Back To School!
Editor's Notes
- #6: x-y < 5