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Linear Equations: Understanding Algebraic Concepts and Graphing

Dive into the world of linear equations and algebra. Learn to solve equations, graph linear relationships, and work on real-world applications. Develop a solid understanding of variables, graphing, and the Cartesian plane to master linear equations.

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Linear Equations: Understanding Algebraic Concepts and Graphing

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  1. Mental Math Mental Math March 3rd -Your next hand-in day will be Wednesday, March 12th- Solve each equation using the distributive property. Show ALL of your steps and verify please. 2(x + 3) = 9 + x 2(2x+1) = 3x + 8 2(2x + 3) = x + 9

  2. achievement achievement NA/CO – not applicable, doesn’t affect your mark IN– incomplete, registering as 0 Blank– missing, special circumstance Highlighted – missing work from Term 2 that can be handed in - Term 1 work cannot be handed in anymore

  3. Test review Test review Retest Day –THURSDAY, March 6th • In order to be eligible for a retest you MUST • Attend a review day on Wednesday • Have ALL missing assignments from Term 2 handed in

  4. Test review Test review

  5. Linear relations Linear relations - Algebra, Variables, Graphing - Approximately March 3rd to March 26th

  6. Intro Intro This unit will help you develop an understanding ofEquations & Linear Relationships. This will help you understand the linear relationships that exist in our world. We will learn how to work with: • Equations and Inequalities • Representing Linear Equations • Real-World Application

  7. Intro Intro REVIEW Cartesian Plane Writing Points Plotting Points

  8. Linear Equations Linear Equations What Are They!? • A type of equation with variables (ex) y = 2x + 1 • When we solve it, we can graph it to form a straight line! Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

  9. Linear Equations Linear Equations What Are They!? • An equation/function is linear if the rate of change is constantbetween any two variables • The variables are points on the Cartesian Plane Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

  10. Linear Equations Linear Equations What Do They Look Like? Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

  11. Linear Equations Linear Equations What Do They Look Like? Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

  12. Linear Equations Linear Equations What Do They Look Like? LINEAR! Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

  13. Linear Equations Linear Equations What Do They Look Like? LINEAR! Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

  14. Mental Math Mental Math March 4th - Your next hand-in day will be Wednesday, March 12th- Copy & complete the table of values, given the equation: y = 2x-5

  15. Linear Equations Linear Equations What Do They Look Like? LINEAR! Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

  16. Linear Equations Linear Equations What Do They Look Like? NON-LINEAR! Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

  17. Linear Equations Linear Equations What Do They Look Like? NON-LINEAR! Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

  18. Linear Equations Linear Equations Slope Intercept • The most common way to simplify linear equations is written as: y=mx+b Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

  19. Linear Equations Linear Equations Slope Intercept The equation of a linear relation is: y = -3x + 5 • Create a table of values • Plot the values on the table • Graph the line *In our formula, y = mx + b, what does each variable mean? Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

  20. Mental Math Mental Math March 5th - Your next hand-in day will be Wednesday, March 12th- Using the following table of values, plot the coordinates on a Cartesian Plane. Is it a linear equation? If so, is it positive or negative?

  21. Linear Equations Linear Equations Slope Intercept Y= y-axis (how far up) X= x-axis (how far along) M= slope (how steep) B= where it crosses the y-axis Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

  22. Linear Equations Linear Equations Slope Intercept M= slope (how steep) • Determined by rise run (ex) m = Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

  23. Linear Equations Linear Equations Slope Music Video! http://www.youtube.com/watch?v=qnMaWTmdbKk

  24. Linear Equations Linear Equations Slope Intercept Practice Y=3x -7 Y=-2x +5 Y=5/3x -2 Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

  25. Linear Equations Linear Equations Slope Intercept Practice Y=3x -7 Y=-2x +5 Y=5/3x -2 Linear Equations. (2013). Uploaded by Math Is Fun. Available online at: http://www.mathsisfun.com/algebra/linear-equations.html

  26. Linear Equations Linear Equations Graph Music Video! http://www.youtube.com/watch?v=2BHzXItkByU&safe=active

  27. Linear Equations Linear Equations Let’s Practice! http://www.mathopolis.com/questions/q.php?id=358&site=1&ref=/equation_of_line.html&qs=358_359_517_518_1156_1157_3204_3205_3206_3207

  28. Mental Math Mental Math March 10th - Your next hand-in day is Wednesday, March 12th- Using the following table of values, plot the coordinates on a Cartesian Plane. Create an equation to represent the line. Hint* y=mx+b

  29. Linear Equations Linear Equations Worksheet Example When a tow truck is called, the cost of the service is $10 plus $1 per mile that the car must be towed. Write and graph a linear equation to represent the total cost of the towing service, which is dependent on the number of miles the car is towed. Find and interpret the slope and y-intercept of the linear equation

  30. Linear Equations Linear Equations Slope Intercept Practice y = 2x-3 m = ___________ y-int= ___________ y = 2/3x-2 m = ___________ y-int = ___________

  31. Linear Equations Linear Equations Slope Intercept Practice Complete the Slope Intercept Practice Worksheet. Any work can be included on a piece of loose-leaf.

  32. Linear Equations Linear Equations Using Graphs to Estimate Values Interpolate • Used to estimate values that lie between 2 known data points Extrapolate • Extending a graph to make predictions

  33. Bob jogs on a running track at a consistent speed. This graph shows how far he runs in 12 mins. - How long will it take to run 2000m? - How far does he job in 10 mins?

  34. How much money did Jenn originally borrow? • How much money does she still have to payback at 3 weeks? • How many weeks does it take for her to payback half?

  35. What is the value of y when x=5 • What is the value of x when y=3

  36. Linear Equations Linear Equations Extrapolate/Interpolate Practice Complete the Extrapolate/Interpolate Practice Worksheet. Due at the start of class on Wednesday.

  37. Mental Math Mental Math March 12th - Hand-In Day!! Pick a Mental Math from Mar 3rdto today - Draw a negative line on a Cartesian Plane. Create an appropriate Table of Values that fits your line (3 points) Create an equation to represent the line. Hint* y=mx+b

  38. Mental Math Mental Math March 17th - Your next hand-in day will be Monday, March 24th - Please state the new formula we have been using in the last half of this unit. In your own words, explain what each variable represents in this equation. Draw a graph to accompany your explanation.

  39. Linear Equations Linear Equations Practice Inverse of: • Addition • Multiplication • Squares Balancing Equations • For our purposes, we want to try & isolate the variable (get the letter all by itself) • If there is an operation being applied to a variable, we must use the oppositeoperation(inverse)

  40. Linear Equations Linear Equations Balancing Equations • Remember, what we do to one side, we must also do to the other side in order to maintain balance (ex) x – 3 = 2 x – 3 + 3 = 2 + 3 x = 2 + 3 x = 5

  41. Linear Equations Linear Equations Balancing Equations (ex) x + = x + - = - x = - x = - x =

  42. Linear Equations Linear Equations Balancing Equations (ex) 6x = 5x + 16 6x – 5x = 5x – 5x + 16 6x – 5x = 16 1x = 16

  43. Linear Equations Linear Equations Balancing Equations (ex) = 6 2 () = 6(2) x = 12

  44. Linear Equations Linear Equations Balancing Equations (ex) x2 = 49 x2 = 49 x = 7

  45. Linear Equations Linear Equations Balancing Equations On your mini-whiteboard, please show how to solve for: (ex) 2x + 1 = 9 2x = 9 -1 2x = 8 = x = 4

  46. Linear Equations Linear Equations Balancing Equations On your mini-whiteboard, please show how to solve for: (ex) - 6 = 3 = 3 + 6 = 9 4() = 9(4) x = 36

  47. Linear Equations Linear Equations Balancing Equations On your mini-whiteboard, please show how to solve for: (ex) 3 – 2x = -11 -2x = -11 - 3 -2x = -14 = x = 7

  48. Mental Math Mental Math March 18th - Your next hand-in day will be Monday, March 24th - Please solve the following, show ALL of your steps: A ) x – 12 = 2 B ) 2x + 7 = 21

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