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Math Education: Solving and Graphing Linear Equations

Math Education: Solving and Graphing Linear Equations. HOME. HOME. Practice. Home Information Movie Review. Practice Quiz References . HOME. Info. QUIZ. Movie. Review. Target Audience. HOME. High School Math Students (grades 9-10) Math Teachers College Students

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Math Education: Solving and Graphing Linear Equations

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  1. Math Education:Solving and Graphing Linear Equations HOME

  2. HOME Practice • Home • Information • Movie • Review • Practice • Quiz • References HOME Info QUIZ Movie Review

  3. Target Audience HOME High School Math Students (grades 9-10) Math Teachers College Students Teacher Assistants

  4. Learning Environment HOME Math Courses Reference for homework Computer labs Review In Class Lesson

  5. Objectives This power point offers a section of information, review, practice, a movie, and a quiz to help teach anyone how, when and why linear expressions and equations are used. I expect the learner be able to score at least a 80% on the quiz after they’ve reviewed this power point. HOME

  6. Information HOME This section of the power point will give you the knowledge to be able to solve and understand the uses of different linear expressions.

  7. LINEAR? The word “linear” pertains to something only having one dimension. It’s a straight line. When a linear equation is correctly graphed it forms a straight line on a graph! Amazing, right?!? HOME

  8. Some questions you may have in your head as we begin this lesson…. • What is a linear equation? • What is an inequality and what do they have to do with linear expressions? • Why will I ever need to learn this material? Lets move forward to answer all these questions and any others you might have! HOME

  9. What is a linear equation?? Do any of the equations on the chalk board look like they couldbe linear equations? Well, lets find out!!! HOME

  10. A linear equation is….. An algebraic equation, such as y = 2x + 7 or 3x + 2y − z = 4, in which the highest degree term in the variable or variables is of the first degree. The graph of such an equation is a straight line if there are two variables. It is often written in the form of y=mx+b HOME

  11. What is an inequality and what do they have to do with linear expressions? A Linear Inequality involves a linear expression in two variables by using any of the relational symbols such as <, >, ≤ or ≥ . It also divides a plane into two parts. HOME

  12. Linear Inequalities... If the boundary line is solid, then the linear inequality must be either ≥ or ≤. HOME

  13. Linear Inequalities... If the boundary line is dotted, then the linear inequality must be either > or <. HOME

  14. Let’s talk about how such expressions could be important to you… • Physics • Conversion of Units • Economics • Engineering • Chemistry • Statistics The things listed to the left are all ways people use linear equations in life and can be clicked on to take you to that specific description. HOME

  15. Physics HOME Physics A simple example from physics is Hooke's law, which states the force of a spring is proportional to the distance it is extended or compressed.

  16. Temperature Conversion of Units Fahrenheit and Celsius are convertible by a linear equation: F - 32 = 9 C / 5. HOME

  17. Economics Economics Total cost is often a function of fixed cost plus variable cost times some variable quantity (or the sum or such products). HOME

  18. Engineering Engineering The heat transfer through a material is proportional to the thickness of the material. HOME

  19. Chemistry Chemistry The gas equation, PV=nRT, when two of the four variables are known, often because they are selected, becomes a linear equation. HOME

  20. Statistics Statistics In statistics, linear regression is a common model for testing correlation. Assumptions of the model, including linearity, make testing computationally much simpler. HOME

  21. Examples of Non-Linear Expression • x ^ 2 • 2xy + 4 • 2x / y • x ^ ½ • No variables can be squared • Variables can’t be multiplied together • Variables can’t be divided by each other • Can not take the square root of variables HOME

  22. Examples of Linear Equations • 2x = 4 • x + 2 = y • 2x + 4y = 6 • Can have one variable • Can have 2 variables • Can be an inequality HOME

  23. Movie on how to solve a linear equation HOME

  24. This is what we know • We’ve gone over what a linear equation is. • What inequalities are and how they relate to linear expressions. • And where these could be used for jobs and everyday life. Lets go over how to do a few problems! HOME

  25. Review Question 2x + 2 = 10 • 2x +2 -2 = 10 -2 • 2x /2 = 8 /2 • X = 4 HOME

  26. Review Question 4x - 4y = 8 • 4x – 4y +4y = 8 +4y • 4x -8 = 4y -8 • 4x /4 – 8 /4 = 4y /4 • x – 2 = y HOME

  27. Review Question 4x – 2y > 12 • 4x – 2y +2y > 12 +2y • 4x -12 > 12 -12 +2y • 4x /2 – 12 /2 > 2y /2 • 2x – 6 > y HOME

  28. Review Question Graph y = 3x + 1 • First, graph the y-intercept point on the y-axis “up 1” • Then begin graphing the slope “up 3, over 1” and “down 3 left 1” • Finally draw a line through the points HOME

  29. On your own! Now that you’ve watched a movie and have seen some example problems on solving a linear equation why don’t you try a few on your own!? Just click to the next slide, then try to solve the problem on your own. When ready to view the answer click the arrow! HOME

  30. Practice…practice…practice… 2x + 3 = 15 HOME

  31. Solution • 2x + 3 = 15 • 2x + 3 -3 = 15 -3 • 2x /2 = 12 /2 • x = 6 HOME

  32. Practice…practice…practice… 3x – 2y = 14 HOME

  33. Solution • 3x – 2y = 14 • 3x – 2y +2y = 14 +2y • 3x -14 = 14 -14 +2y • 3x /2 - 14 /2 = 2y /2 • y = 3x/2 - 7 HOME

  34. Practice…practice…practice… 2x + 8 > 4 HOME

  35. Solution • 2x + 8 > 4 • 2x + 8 -8 > 4 -8 • 2x /2 > -4 /2 • x > -2 HOME

  36. Practice…practice…practice… Graph: Y = 2x + 4 HOME

  37. Solution • y = 2x + 4 • First, plot the point (0, 4) • Then, plot the points “up 2 over 1” and then “down 2 left 1” • Finally, complete the grapy by drawing a line through the points HOME

  38. Practice…practice…practice… Graph: Y > 2x/3 + 2 HOME

  39. Solution • First, plot the point (0, 2) • Then, plot the points “down 2 over 3” and then “up 2 left 3” • Next, complete the grapy by drawing a line through the points • Finally, since it’s a less than sign, shade underneath the line HOME

  40. Quiz!!! You’ll be given 10 questions based off what you’ve learned from this power point. There are two choices to pick from and you must correctly answer each one to move on. Click on whichever one you think is correct to find the answer. GOOD LUCK!!! HOME

  41. Question #1 • 6x – 12 = -24 • x = -2 • x= -6 HOME

  42. CORRECT HOME

  43. WRONG HOME

  44. Question #2 • 5x – 10 = 90 • x = 16 • x = 20 HOME

  45. CORRECT HOME

  46. WRONG HOME

  47. Question #3 • 6x – 2y = -10 • y = 3x + 5 • y = -3x - 5 HOME

  48. CORRECT HOME

  49. WRONG HOME

  50. Question #4 • 3x + 3y = 12 • y = 6x - 4 • y = -x + 4 HOME

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