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Graphing linear equations

Learn how to solve linear equations for Y in order to graph them accurately following a step-by-step guide. Understand how to manipulate equations and graph the linear functions effectively.

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Graphing linear equations

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  1. Graphing linear equations By Robert O. Mills Jr. Hermitage High School Henrico County Public Schools

  2. Part One Solving for Y

  3. In order to graph a linear equation you must first solve for y.

  4. Given the Problem : x+y=4

  5. First check to see if y is + or –. x+y=4 If y is + you leave it alone.

  6. What number or factor is on the same side of the equation as + y? x+y=4

  7. Move that number or factor to the other side of the = and change its sign. x+y=4

  8. Move that number or factor to the other side of the = and change its sign. y=4-x

  9. Your answer is: y=4-x

  10. Given the Problem : x-y=4

  11. First check to see if y is + or –. x-y=4 If y is - you move y to the other side of the = and change it to +y.

  12. x-y=4

  13. x=4+y

  14. What number or factor is on the same side of the equation as + y? x=4+y

  15. Move that number or factor to the other side of the = and change its sign.

  16. x = 4 + y

  17. x-4=y Your answer is:

  18. x-4 =y or y=x-4

  19. Given the Problem : x+2y=4

  20. First check to see if y is + or –. x+2y=4 If y is + you leave it alone.

  21. What number or factor is on the same side of the equation as + y? x+2y=4

  22. Move that number or factor to the other side of the = and change its sign. x+2y=4

  23. Move that number or factor to the other side of the = and change its sign. 2y=4-x

  24. If the +y factor has a co-efficient it must lose it. The factors and numbers on the opposite side of the = become a fraction with the y co-efficient as the denominator. 2y=4-x

  25. If the +y factor has a co-efficient it must lose it. The factors and numbers on the opposite side of the = become a fraction with the y co-efficient as the denominator.

  26. Given the Problem : 2x-2y=4

  27. First check to see if y is + or –. 2x-2y=4 If y is - you move y to the other side of the = and change it to +y.

  28. 2x-2y=4

  29. 2x=4+2y

  30. What number or factor is on the same side of the equation as + y? 2x=4+2y

  31. Move that number or factor to the other side of the = and change its sign.

  32. 2x=4+2y

  33. 2x-4=2y Your answer is:

  34. 2x-4 =2y or 2y=2x-4

  35. If the +y factor has a co-efficient it must lose it. The factors and numbers on the opposite side of the = become a fraction with the y co-efficient as the denominator. 2y=2x-4

  36. If the +y factor has a co-efficient it must lose it. The factors and numbers on the opposite side of the = become a fraction with the y co-efficient as the denominator.

  37. Advanced Level • There are times when it will be necessary to work the equation to a simpler level. • For example the formula for slope intercept is y = mx + b. Any denominator in this case must be eliminated. How to do this?

  38. Most often when we think of the distributive property, we are thinking of using it with ( ) and the operation is multiplication. In the previous example the line is also a grouping tool with the operation division.

  39. This is a more complex problem.

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