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Understanding Linear Equations: Graphing, Solving, and Using Tables

This article explains the concept of linear equations, including how to graph them, solve for y, and use tables. It also covers the definition of slope and how to write equations in point-slope form. Additionally, it discusses horizontal and vertical lines, parallel lines, and perpendicular lines.

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Understanding Linear Equations: Graphing, Solving, and Using Tables

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  1. Bellringer

  2. WE WILL LEARN

  3. USE TABLES ALWAYS!!!

  4. Most of the equations we deal with from now on are LINEAR equations • All linear equations (except vertical lines) have a slope.

  5. When asked to graph… solve the equation for y, and then use the slope, and the y-intercept • OR…you can plug in a number for x (independent) and get a number for y (dependent) and then you have (x, y) to put on your graph.

  6. Use slope intercept form to set up tables or make a graph

  7. Let’s try some…Graph

  8. Definition of Slope The slope of the line through the distinct points (x1, y1) and (x2, y2) is where x2 – x1 = 0. y Run x2 – x1 Change in y Rise y2 – y1 = = y2 Change in x Run x2 – x1 Rise y2 – y1 (x2, y2) y1 (x1, y1) x x1 x2 Definition of Slope

  9. Honors HW2.2 page 67-69 • 9, 10, 34, 36, 46, 48, 61, 80, 81, 82

  10. HW Section 2.2 page 67-682-8 even, 32-36 even,42-46 even

  11. Bellringer

  12. Day Two Point slope form (how to write your own equations)

  13. Let’s find the slope of the line that connects these two points

  14. m = -1 • m = 3/6, but better to write m = 1/2

  15. Do one of these

  16. If you are asked to write an equation, use point slope form

  17. When I say, “what two things do you need to write an equation”You say, “A point and a slope

  18. Write an equation for the line through this pair of points

  19. Write an equation for the line through this pair of points

  20. Write an equation for the line through this pair of points

  21. Write an equation for the line through this pair of points

  22. Zero Slope Positive Slope y y m > 0 m = 0 x x Negative Slope Undefined Slope y y Line rises from left to right. Line is horizontal. m is undefined m < 0 x x Line falls from left to right. Line is vertical.

  23. A vertical line is given by an equation of the form x = a EX: where a is the x-intercept. Equation of a Vertical Line

  24. A horizontal line is given by an equation of the form y = b, EX: where b is the y-intercept. Equation of a Horizontal Line

  25. Parallel Lines Have the Same Slope!!!

  26. Perpendicular Slopes are Opposite (one positive and one negative) and Reciprocals (flips of each other)

  27. Write the equation for the line:

  28. Write the equation for the line:

  29. Write the equation for the line:

  30. Write the equation for the line:

  31. HW Section 2.2p. 68 • 26-31, 51, 53, 66, 68

  32. Honors HW2.2 p. 68 • 28, 30, 66, 68, 85 - 90

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