1 / 71

Algebra Chapter 5

Algebra Chapter 5. Writing Linear Equations. Writing linear equations in slope-intercept form—5.1. Slope-Intercept Form. m is slope b is y-intercept y=mx + b. Writing the equation of a line. Write an equation whose slope is 2 and it’s y-intercept is -3.

wood
Télécharger la présentation

Algebra Chapter 5

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. AlgebraChapter 5 Writing Linear Equations

  2. Writing linear equations in slope-intercept form—5.1

  3. Slope-Intercept Form • m is slope • b is y-intercept • y=mx + b

  4. Writing the equation of a line • Write an equation whose slope is 2 and it’s y-intercept is -3

  5. Writing the Equation of a line • Find the equation of the line whose slope is ½ and y-intercept is 9

  6. Writing Equations from Graphs • -Graph the points and count slope • -Use slope equation

  7. Writing Equations from Graphs • Write the Equation of the line that passes through the point (-2, 0) and has a y-intercept of -1

  8. Writing Equations from Graphs • Write the Equation of the line that passes through the point (4, 1) and has a y-intercept of 1

  9. Writing Equations from Graphs • Write the Equation of the line that passes through the points (0 , 2) and (3, -3)

  10. Writing Equations from Graphs • Your cell phone plan costs $40 per month for 500 minutes, and $1.20 for each minute over 500. Write and graph an equation that models your costs

  11. p.276#9-25 All

  12. Writing equations given slope and point—5.2

  13. Solving Equations • In any equation, we can solve for any variable that is not known • -Rewrite in terms of that variable • -Find a value if all the other values are known • -Can use this to find equations

  14. Solving With Slope and a Point • We can find the equation of any line simply by knowing a point on the line and it’s slope.

  15. Solving With Slope and Point • Substitute known values into the equation • Solve for b • Rewrite the equation y = mx + b with slope and y-intercept values

  16. Solving with Slope and Point • Find the equation of the line passing through the point (-3, 0 ) and has slope of 1/3

  17. Solving with Slope and a Point • Find the equation of the line passing through point (-2, -1) with slope of -3

  18. Solving with Slope and a Point • Find the equation of the line passing through (3 , -4) and is parallel to the line y = -3x – 2

  19. p.282 #12-40 Even

  20. Writing linear equations given two points—5.3 (Day 1)

  21. Finding Slope… • We can find slope 2 ways • -Graphing • -Slope equations

  22. Finding Slope.. • Find the slope of the line through the points (4, 1) and (-1, 5)

  23. Finding Slope.. • Find the slope of the line through the points (0 , -1) and (5, 9)

  24. Finding Slope.. • Find the slope of the line through the points (3 , 4) and (3 , 9)

  25. So…Writing Equations Now… • When Given 2 points, first find the slope. • Once you find the slope, you have a slope and a point (2 points actually!) • Plug in the slope and a point to find the equation

  26. Hold up… • If we have two points, does it matter which one we choose? • No…Since both points are on the line, doesn’t matter which one we choose.

  27. Writing Equations • Find the equation of the line passing through the points: • (0 , -1) and (5 , 9)

  28. Writing Equations • Find the equation of the line passing through the points: • (1 , 6) and (3 , -4)

  29. Writing Equations • Find the equation of the line passing through the points: • (6 , -3) and (0 , 9)

  30. Writing Equations • Find the equation of the line passing through the points: • (3 , -6) and (3 , 4)

  31. p.288 #21-32

  32. Writing linear equations with two given points—5.3 (day 2)

  33. Perpendicular Lines • What is perpendicular? • Why/How are lines perpendicular?

  34. Perpendicular Lines • Draw some pictures!

  35. What do you think? • We’ve been talking a lot about slope… • … is there a way we can represent perpendicular lines in terms of slope?

  36. Perpendicular Lines • Two lines are perpendicular iff their slopes are negative reciprocals of each other • -What is a reciprocal • -What then makes it a negative reciprocal?

  37. Perpendicular Lines • Slopes: Perp. Slope: • 3 • ½ • -1/4 • -5/7

  38. Equations of Perp. Lines • Find the equation of the line with a y-intercept of 3 and is perpendicular to the line:

  39. Equations of Perp. Lines • Find the equation of the line with a y-intercept of 1 and is perpendicular to the line:

  40. Equations of Perp. Lines • Find the equation of the line passing through the point ( 3, 4) and is perpendicular to the line:

  41. p.289 #36-47

  42. Fitting a line to data—5.4

  43. Class Activity!  • Including yourself, go around the class and ask everyone their height and the length of their hand. Graph the data on graph paper!

  44. What did you find? • Is there a relationship between the data? • Can you draw a line through your graph that accurately represents your graph? • Can you find the equation of that line?

  45. Best Fitting Lines • What you drew was a Line of Best Fit (Best Fitting line!) • Is there only 1 correct answer? • -For now: No • -Technically….yes • Least Squares Method or Linear Regression

  46. Correlation • Data is Positively Correlated iff the line drawn through the data has a positive slope • Examples:

  47. Correlation • Data is Negatively Correlated iff the line drawn through the data has a negative slope • Examples:

  48. Correlation • Data has No Correlation iff there cannot be an accurate line drawn through the data • Examples:

  49. p.296 #13-24

  50. Point-slope form of a linear equation—5.5

More Related