Computer Science Output for Quarter 1 - Week 6 & 7
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This document discusses linear equations in two variables. It defines a linear equation as an equation that can be written in the standard form of ax + by = c, where a, b, and c are real numbers and a and b are not both equal to 0. The document provides examples of determining if equations are linear and writing them in standard form. It also discusses how to determine if an ordered pair is a solution to a linear equation and how to graph linear equations using tables of values, x- and y-intercepts, and slope-intercept form.
Computer Science Output for Quarter 1 - Week 6 & 7
- 1. Linear Equations in Two Variables Grade 8 – Mathematics GHABRIEL B. DIVINOSA 8-BANABA
- 2. Objectives: • illustrate linear equations in two variables; • determine if an ordered pair is a solution of the given linear equation; • graph linear equations in two variables.
- 3. LET’S WATCH THIS VIDEO FROM DEPED TV: https://www.youtube.com/watch?v=PrTIK9nv650
- 4. Linear Equations in Two Variables An equation that can be written in standard form ax + by = c where a, b, and c are real numbers but a and b are both NOT equal to 0.
- 5. Determine whether or not each equation is a linear equation in two variables. If yes, write it in standard form. 5x + 3y = 6 Yes Already in standard form
- 6. Determine whether or not each equation is a linear equation in two variables. If yes, write it in standard form. x = 7y + 3 x – 7y = 7y – 7y + 3 x – 7y = 3 Yes Standard form
- 7. Determine whether or not each equation is a linear equation in two variables. If yes, write it in standard form. 3x2 – y = 9 No
- 8. Determine whether or not each equation is a linear equation in two variables. If yes, write it in standard form. 3 𝑥 + 𝑦 = 20 No
- 9. Determine whether or not each equation is a linear equation in two variables. If yes, write it in standard form. xy = -5 No
- 10. Determine whether or not each equation is a linear equation in two variables. If yes, write it in standard form. 𝑥 3 + 𝑦 6 = 1 Yes
- 11. Solutions of a Linear Equations in Two Variables These are ordered pairs (x, y) that make the equation true.
- 12. Determine whether (3, -2) is a solution of the equation 5y = -2x – 4. 5y = -2x – 4 5(-2) = -2(3) – 4 -10 = -6 – 4 -10 = -10 YES
- 13. Determine whether (-1, 4) is a solution of the equation 6x + 2y = 3 6x + 2y = 3 6(-1) + 2(4) = 3 -6 + 8 = 3 2 ≠ 3 NO
- 14. Answer Skill Builder on page 76.
- 15. Skill Builder on p. 76 -y = 4x + 7; (-1, -3) -(-3) = 4(-1) + 7 3 = -4 + 7 3 = 3 YES
- 16. Skill Builder on p. 76 -y = 4x + 7; (2, 15) -(15) = 4(2) + 7 -15 = 8 + 7 -15 ≠ 15 NO
- 17. Skill Builder on p. 76 -y = 4x + 7; (0, 7) -(7) = 4(0) + 7 -7 = 0 + 7 -7 ≠ 7 NO
- 18. In reality, why do you think checking whether a solution to a problem is correct is essential? Expound.
- 19. Graphing Linear Equations in Two Variables Three Ways: 1. Table of Values 2. x – and y – intercepts 3. Slope and one point
- 20. Graph y = 4x – 2 using table of values. x y = 4x – 2 y (x, y) -1 0 1 y = 4(-1) – 2 -6 (-1, -6) - 2 y = 4(0) – 2 (0, -2) (1, 2) y = 4(1) – 2 2
- 21. (-1, -6) Graph y = 4x – 2 (-1, -6) (0, -2) (1, 2) (0, -2) (1, 2) y = 4x – 2
- 22. Graph x – y = 3 using table of values. x x – y = 3 y (x, y) -2 1 3 -2 – y = 3 -5 (-2, -5) - 2 1 – y = 3 (1, -2) (3, 0) 3 – y = 3 0
- 23. (-2, -5) Graph x – y = 3 (3, 0) (1, -2) x – y = 3 (-2, -5) (1, -2) (3, 0)
- 24. Graphing Linear Equations in Two Variables in Two Variables using x – and y - intercepts
- 25. x – intercept is the point where a line crosses the x - axis To solve for the x – intercept, let y = 0 and solve for x. Example: Find the x – intercept of x - 2y = 4 y = 0 x – 2(0) = 4 x = 4 The graph of x – 2y = 4 will cross the x – axis at (4, 0)
- 26. y – intercept is the point where a line crosses the y - axis To solve for the y – intercept, let x = 0 and solve for y. Example: Find the y – intercept of x - 2y = 4 x = 0 0 – 2𝑦 = 4 −2𝑦 −2 = 4 −2 y = - 2 The graph of x – 2y = 4 will cross the y – axis at (0, -2)
- 27. Graph x – 2y = 4 (4, 0) (0, -2) x – 2y = 4 (4, 0) (0, -2)
- 28. Graph x – y = 3 using x – and y - intercept. x x – y = 3 y (x, y) 0 3 0 – y = 3 -3 (0, -3) 0 x – 0 = 3 (3, 0)
- 29. Graph x – y = 3 (3, 0) (0, -3) x – y = 3 (0, -3) (3, 0)