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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.

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Algebra Chapter 5

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  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

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