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Understanding the Equation of a Line: Slope and Y-Intercept Explained

Dive into the fundamentals of linear equations with a focus on the slope-intercept form, where the equation of a line is expressed as y = mx + b, with m representing the slope and b the y-intercept. Learn how to find the equation of a line using two essential pieces of information, such as slope and a point on the line, or the y-intercept and another point. Explore various examples, graphs, and practice problems to solidify your understanding of line equations, slopes, and intercepts. Perfect for students and anyone interested in algebra!

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Understanding the Equation of a Line: Slope and Y-Intercept Explained

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  1. Equation of a Line Wednesday

  2. Wayward Wednesday • Why is the sky blue?

  3. Slope Slope = rise run We call slope the variable m

  4. Y-intercept The y-intercept occurs where x = 0 We call the y-intercept b

  5. Equation of a Line y = mx + b slope y-intercept

  6. Equation of a Line Graph: y = ½x + 3 slope y-intercept

  7. Equation of a Line Graph: y = ½x + 3 slope y-intercept

  8. Equation of a Line Graph: y = –2x + 5 slope y-intercept

  9. Equation of a Line Graph: y = –2x + 5 slope y-intercept

  10. Equation of a Line Find the equation: y = mx + b slope y-intercept

  11. Equation of a Line Find the equation: y = –1x + 3 slope y-intercept

  12. Equation of a Line Find the equation: y = mx + b slope y-intercept

  13. Equation of a Line Find the equation: y = 2x – 2 slope y-intercept

  14. Equation of a Line Find the equation: y = mx + b slope y-intercept

  15. Equation of a Line Find the equation: y = (2/3)x + 0 slope y-intercept

  16. Finding the Equation of a Line • All you ever need is two unique pieces of information to figure out the equation of a line. Example: Let’s say you know the slope is ¾ and the y-intercept is ½. Then the equation of the line is: y = mx + b

  17. Finding the Equation of a Line • All you ever need is two unique pieces of information to figure out the equation of a line. Example: Let’s say you know the slope is ¾ and the y-intercept is –½. Then the equation of the line is: y = ¾x –½

  18. Finding the Equation of a Line • All you ever need is two unique pieces of information to figure out the equation of a line. Example: Let’s say the slope is 2 and a point on the line is (3, 7) y = mx + b

  19. Finding the Equation of a Line • All you ever need is two unique pieces of information to figure out the equation of a line. Example: Let’s say the slope is 2 and a point on the line is (3, 7) y = 2x + b

  20. Finding the Equation of a Line Example: Let’s say the slope is 2 and a point on the line is (3, 7) (7) = 2(3) + b 7 = 6 + b 7– 6 = b b = 1

  21. Finding the Equation of a Line Example: Let’s say the slope is 2 and a point on the line is (3, 7) y = 2x + 1

  22. Finding the Equation of a Line Example: Let’s say the y-intercept is (0, -4) and a point on the line is (2, -9) y = mx + b

  23. Finding the Equation of a Line Example: Let’s say the y-intercept is (0, -4) and a point on the line is (2, -9) y = mx – 4

  24. Finding the Equation of a Line Example: Let’s say the y-intercept is (0, -4) and a point on the line is (2, -9) (-9) = m(2) – 4 –9 + 4 = m(2) –5/2 = m

  25. Finding the Equation of a Line Example: Let’s say the y-intercept is (0, -4) and a point on the line is (2, -9) y = (–5/2)x – 4

  26. Finding the Equation of a Line Example: Let’s say we know that the line goes through the points (1, 2) and (3, 8) y = mx + b

  27. Finding the Equation of a Line Example: Let’s say we know that the line goes through the points (1, 2) and (3, 8) y = mx + b Rise Run 8 – 2 3 – 1 6 2 m = = = = 3

  28. Finding the Equation of a Line Example: Let’s say we know that the line goes through the points (1, 2) and (3, 8) y = 3x + b

  29. Finding the Equation of a Line Example: Let’s say we know that the line goes through the points (1, 2) and (3, 8) (2) = 3(1)+ b 2 – 3 = b –1 = b

  30. Finding the Equation of a Line Example: Let’s say we know that the line goes through the points (1, 2) and (3, 8) y = 3x – 1

  31. Practice!

  32. Graph this line! slope = 2 y-intercept = -1

  33. Graph this line! slope = -3 y-intercept = 2

  34. Graph this line! y = 2x – 3

  35. Graph this line! y = x + ½

  36. Graph this line! y = -½x + 3

  37. Graph this line! y = -3x + 2

  38. Graph this line! y – ¼x – 3 = 0 y = ¼x + 3

  39. Graph this line! 2y + 6x = 2 y = -3x + 1

  40. Graph this line! ½y – x + 2 = 0 y = 2x – 4

  41. Homework Page 418 #1 – 8 Page 419 #46 – 55

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