1 / 56

Chapter 2

Chapter 2. Section 3: Quick Graphs of Linear Equations Section 4: Writing Equations of Lines. There are 4 ways to represent any function and 3 ways to write an equation of a line. There are 4 ways to represent any function:. G. raphically/visual. N. umerically/table. A.

conan
Download Presentation

Chapter 2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 2 Section 3: Quick Graphs of Linear Equations Section 4: Writing Equations of Lines

  2. There are 4 ways to represent any function and 3 ways to write an equation of a line.

  3. There are 4 ways to represent any function: G raphically/visual N umerically/table A nalytically/equation W ords/verbally

  4. There are 3 ways to write an equation of a line: S lope-Intercept Form P oint-Slope Form S tandard Form

  5. Open to p. 82 Complete the activity and turn it in

  6. GRAPHING WITH THE SLOPE-INTERCEPT FORM SLOPE-INTERCEPT FORM m = slope and b = y-intercept; (0, b) Plot the point where the line crosses the y-axis Find the slope and use it to plot the 2nd point Draw a line through the two points

  7. Graph the equations using the slope-intercept form. m = b =

  8. Graph the equations using the slope-intercept form. m = b =

  9. Graph the equations using the slope-intercept form. m = b =

  10. USING THE SLOPE-INTERCEPT FORM You are buying an $1100 computer on layaway. You make a $250 deposit and then make weekly payments according to the equation a = 850 – 50t where a is the amount you owe and t is the number of weeks. a. What is the original amount you owe on layaway? • b. What is your weekly payment? • c. Graph the model.

  11. GRAPHING HORIZONTAL AND VERICAL LINES HORIZONTAL AND VERTICAL LINES Horizontal Lines: The graph of y = c is a horizontal line through (0, c) Vertical Lines: The graph of x = c is a vertical line through (c, 0)

  12. P86#21-57x3to be turned in Thur. How many points are required to graph a line? What if the equation is not in slope-intercept form, but is in standard form? Easiest way to graph in standard form is to graph the x-intercept (x, 0) and y-intercept (0, b).

  13. GRAPHING WITH STANDARD FORM STANDARD FORM A and B are not zero Easiest way to graph in standard form is to graph the x-intercept (x, 0) and y-intercept (0, b).

  14. ( , 0) (0, )

  15. ( , 0) (0, )

  16. ( , 0) (0, )

  17. USING STANDARD FORM • The school band is selling sweatshirts and T-shirts to raise money. The goal is to raise $1200. Sweatshirts sell for a profit of $2.50 each and T-shirts for $1.50 each. Describe the numbers of sweatshirts and T-shirts the band can sell to reach the goal. 2.5s+1.5t=1200 Graph the model

  18. WRITING AN EQATION OF A LINE

  19. SLOPE-INTECEPT FORM Given the slope m and the y-intercept b use the equation: y = mx +b

  20. POINT-SLOPE

  21. FORM Given slope m and a point (x1, y1), use this equation: y – y1 =m(x – x1)

  22. TWO POINTS Given two points (x1, y1) and (x2, y2), use the formula: t find the slope m. Then use the slope-intercept form or point-slope form with the slope and either point of the given points to write an equation of a line.

  23. WRITING AN EQUATION GIVEN THE SLOPE AND Y-INTERCEPT

  24. 4. m = -3 and b = 6 5. m = and b = -8 6. m = 4 and b = 3

  25. WRITING AN EQUATION GIVEN THE SLOPE AND POINT

  26. 7. Write an equation of the line that passes through (2, 3) and has a slope of .

  27. SLOPE-INTERCEPT FORM

  28. 8. Write an equation of the line that passes through (5, 4) and has a slope of -3.

  29. SLOPE-INTERCEPT FORM

  30. WRITING EQUATIONS OF PERPENDICULAR AND PARALLEL LINES

  31. Write an equation of a line that passes through (3, 2) and is (a) perpendicular and (b) parallel to the line y = -3x + 2.

  32. PERPENDICULAR PARALLEL

  33. Write an equation of a line that passes through (-2, 3) and is (a) perpendicular and (b) parallel to the line y = -4x + 1.

  34. PERPENDICULAR PARALLEL

  35. WRITING AN EQUATION GIVEN TWO POINTS

  36. Write an equation of the line that passes through (-2, -1) and (3, 4).

  37. SLOPE-INTERCEPT FORM

  38. 12. Write an equation of the line that passes through (5, -2) and (2, 10).

  39. SLOPE-INTERCEPT FORM

  40. WRITING DIRECT VARIATON EQATIONS

  41. DIRECT VARIATION EQUATION y = kx and k 0.

  42. The nonzero constant k is called constant of variation and y is said to vary directly with x. The graph of y = kx is a line through the origin.

  43. WRITING AND USING A DIRECT VARIATION EQUATION

  44. The variables x and y vary directly, and y = 12 and x = 4.

  45. 13a. Write and graph an equation relating x and y. 13b. Find y when x = 5.

  46. The variables x and y vary directly, and y = 8 and x = -4.

  47. 14a. Write and graph an equation relating x and y. 14b. Find x when y = 2.

  48. IDENTIFYING DIRECT VARIATION

  49. Tell whether the data show direct variation. If so, write an equation relating and y.

More Related