Lecture 2.1 2.2a bt

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Lecture 2.1 2.2a bt

  1. 1. Today’s Agenda • Attendance / Announcements – Exam 1 – Tuesday 9/24 • Covers Chapters 1.1 to 2.4 (skip 2.5) • Questions from HW? • Section 2.1, 2.2a • Quiz • Have a good weekend (Go Birds!)
  2. 2. Graphing on the Coordinate Plane Quadrant I (+, +) Quadrant II (-, +) Quadrant IV (+, -) Quadrant III (-, -) (x, y)
  3. 3. Coordinate Points (x, y)
  4. 4. Equations of two variables To “solve” this, we need to find values of both x and y that satisfy the equation. 32xy We then write these solutions as coordinate points (ordered pair)
  5. 5. Equations of two variables For most multi-variable equations, there can be an infinite number of solutions. 32xy
  6. 6. Equations of two variables First, can we find any solutions to this equation? 32xy
  7. 7. Equations of two variables Next, we need to be able to verify if an ordered pair is a solution to the equation 32xy
  8. 8. Equations of two variables 32xy
  9. 9. Graphing Equations To graph an equation in two variables is to plot the points whose ordered pairs are solutions to the equation This can be done with a “T-Chart”
  10. 10. Sketch the Graph of 3xy
  11. 11. Sketch the Graph of 243 yx
  12. 12. Intercepts The x-intercept of a graph is the x- coordinate of where the graph crosses the x-axis The y-intercept of a graph is the y- coordinate of where the graph crosses the y-axis
  13. 13. Intercepts To find the x-intercept: • Set y = 0 • Solve for x To find the y-intercept: • Set x = 0 • Solve for y 0,x y,0
  14. 14. Find the intercepts of… 1232 yx
  15. 15. Find the intercepts of… 165 2 xxy
  16. 16. Reading Graphs
  17. 17. Reading Graphs
  18. 18. 2.2a Equations of Lines Slope – slope of a line through two points (x1,y1) and (x2,y2) is: m run rise xinchange yinchange 12 12 xx yy x y
  19. 19. Find the slope of the lines that pass through the points… 4,58,6 and 9,23,4 and 11,42,5 and 12 12 xx yy m
  20. 20. Slope-Intercept Form of a Line (p. 90) bmxy Slope of the line y-intercept of the line
  21. 21. We can use this as a graphing technique 43xy
  22. 22. We can use this as a graphing technique xy 4
  23. 23. We can use this as a graphing technique 269 yx
  24. 24. We can use this as a graphing technique 2 5 2 3 xy
  25. 25. Classwork / Homework Page 83 1 – 39 odd, 49 – 61 Page 97 1 – 31 odd

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