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Understanding Coordinate Points and Functions in Algebra

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This comprehensive guide focuses on defining and plotting ordered pairs in a coordinate plane, along with identifying quadrants and axes. It includes warm-up questions to reinforce concepts such as equation forms, slope-intercept form, direct variation, and the identification of x- and y-intercepts on graphs. The activity involves plotting points, drawing lines, and understanding the relationships of slopes in various scenarios. Practice exercises and re-teach sections ensure mastery of material related to linear equations, functions, and graphing techniques.

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Understanding Coordinate Points and Functions in Algebra

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  1. Algebra I Chapter 4

  2. Directions: Plot and label the following points. 4. A(4, -1) B (5, 0) 5. A (-2, -3) B (-3, -2) Warm Up

  3. How do you plot an ordered pair? • How do you write an ordered pair? • What are quadrants? • How do we name them? • What is the origin? • What is the vertical axis? • What is the horizontal axis? Re-teach

  4. Directions: Plot and label the ordered pairs in a coordinate plane. 13. A (0,3) B (-2, 1) C (2, 0) 15. A (4, 1) B (0, -3) C (3, 3) 17. A (-4, 1) B (-1, 5) C (0, -4) Practice

  5. Directions: Without plotting, identify the quadrant. 19. (5, -3) 21. (6, 17) 23. (-4, -2) 25. (-5, -2) Practice

  6. Complete the following work on the given worksheet. Warm Up

  7. What is equation form? • How do we rewrite a function to equation form? -3x + y= 12 2x + 3y = 6 x + 4y = 48 Re-teach

  8. Directions: Partner with another person and complete the questions on the flashcard. Practice

  9. 81. 5 + 2 + (-3) 83. -18 + (-10) + (-1) 91. 9x= 3 94. 24 = 8c 97. n/15 = 3/5 Closure ---REPEAT

  10. Finding x- intercepts and y-intercepts of the graph. 2x + 3y = 6 Solving for x. Step 1- Write the original equation. Step 2 – Substitute 0 in for y. Step 3- Solve for x. Re-teach

  11. Finding x- intercepts and y-intercepts of the graph. 2x + 3y = 6 Solving for y. Step 1- Write the original equation. Step 2- Substitute 0 for x. Step 3- Solve for y. Re-teach

  12. Step 4- After you solve for x and y plot your points. Step 5- Draw a quick line Re-teach

  13. Directions: Partner up and get a piece of construction paper. Solve the problems for your group and create a poster of the steps on how to solve. Group 1 Group 2 Group 3 x + 3y = 5 x – 2y = 6 2x + 6y=-24 3x + 4y = 12 5x – y = 45 -x + 3y = 27 Practice

  14. Directions: Plot the points, and draw a line through them. Explain whether the slope is positive, negative or undefined. 12. (6, 9) (4, 3) 17. (0, 0) (-5, 3) 19. (2, -2) (2, -6) Warm Up

  15. Re-teach

  16. Re-teach

  17. Directions: Use the slope formula to find the slope and graph the line. 21. (1, 5) (5, 2) 23. (0, -6) (8, 0) 29. (3, 6) (3, 0) Practice

  18. 45. 4b = 26 – 9b 51. 3x + 12 = 5(x + y) Closure---REPEAT

  19. Re-teach y= kx (model for direct variation) To Find the constant of variation and the slope. Ex: y=-5x (0,0) (1,2) Step 1- Plug the number (-5) in for k. The constant of variation is k=-5 Step 2- Use the slope formula to find the slope.

  20. 12. y=3x 13. -2/5x 15. y=-3x Practice

  21. Examples: Variables x and y vary directly. x=5; y =20 • Write an equation that relates x and y. • Find the value of y when x = 10 Step 1- Write the model for direct variation. Step 2- Substitute 5 in for x and 20 in for y. Step 3- Solve. Step 4- Substitute 10 in for the value of x. Re-teach

  22. Graph the equation:13. y=2x - 115. y = 2/3x33. y = 2 Warm Up

  23. Slope-Intercept Form: y = mx + bSlope is mY intercept is b *** Y IS DIFFERENT THAN THE Y INTERCEPT*** Re-teach

  24. 13. y= 6x + 421. 12x +4y – 2 = 0 Practice

  25. Graphing Equations- Parallel lines- have the same slope Perpendicular lines- have a different slope but the same y intercept Re-teach

  26. Functions: Is it or isn’t it? Practice

  27. f(x) g(x) h(x) What do they mean? 21. g(x) = 8x -2 ; x =2, 2 = 0, x = -3 Re-teach

  28. f(x) g(x) h(x) Directions: Solve the function. 23. g(x) = 1.25x; x =2, 2 = 0, x = -3 27. 2/5x + 7 Practice

  29. Directions: Graph the function. 32. f(x) = -2x + 5 34. h(x) = 5x – 6 38. f(x) 4x + 1 Review--Functions

  30. Directions: Grab a flashcard split into two groups. Solve problems 56-58 on flashcard. Practice

  31. Scatter Plots • Linear Equations • Quick graphs with intercepts • Graphs using slope-intercept form • Solving linear equations • Slope of a line • Direct Variation • Functions Review Chapter Test

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