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Equations of Lines in Standard Form

Learn how to convert equations from slope-intercept to standard form with clear examples and step-by-step instructions for better understanding.

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Equations of Lines in Standard Form

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  1. Bellwork 12/1 • 1.) Write an equation of a line given the points (1,6) & (3,-4) • 1.) Find the Slope • 2.) Plug in one point and the slope. (y - y1) = m(x - x1)

  2. 1.) Write an equation of a line given • The points (1,6) & (3,-4) • 1.) Find the Slope • m = (-4 -6)/(3-1) • m = -10/2 = -5

  3. Write an equation of a line given • The points (1,6) & (3,-4) • 2.) Plug in one of the points (y - y1) = m(x - x1) • (y - 6) = -5(x - 1) • y - 6 = -5x + 5

  4. Write an equation of a line given • y - 6 = -5x + 5 • y - 6 + 6 = -5x + 5 + 6 • y = -5x + 11

  5. Today’s Objective • To be able to Re-Write and equation in Standard Form. • Ax + By = C…… where • A,B & C are real numbers

  6. Equations of Lines • Vertical line x = # • Horizontal line y = # • Slope, y-intercept y=mx+b • Point, Slopey-y1=m(x-x1) • Standard Form Ax+By = C

  7. 1.) Writing an equation in Standard Form Ax + By = C • y = 2/5x - 3 • The 1st step is to multiply both sides by 5. Why?

  8. 1.) Writing an equation in Standard Form Ax + By = C • y = 2/5x - 3 • (5)y = (2/5x - 3)5 • 5y = 2x - 15 • 5y -2x = 2x -2x - 15 • -2x + 5y = -15

  9. Writing an equation in Standard Form Ax + By = C • y = 1/2x + 4 • The 1st step is to multiply both sides by 2. You Try This One

  10. Writing an equation in Standard Form Ax + By = C • y = 1/2x + 4 • (2)y = (1/2x + 4)2 • 2y = x + 8 • 2y -x = x -x + 8 • -x + 2y = 8

  11. 2.) Writing an equation in Standard Form Ax + By = C • y = 0.55x + 1.35 • The 1st step is to multiply both sides by 100. Why?

  12. 2.) Writing an equation in Standard Form Ax + By = C • y = 0.55x + 1.35 • (100)y = (0.55x + 1.35)100 • 100y = 55x + 135 • 100y -55x = 55x -55x + 135 • -55x + 100y = 135

  13. -55x + 100y = 135 • Since all 3 TERMS are divisible by 5, we can simplify by dividing both sides by 5. • (-55x + 100y)/5 = 135/5 • -11x + 20y = 27

  14. Writing an equation in Standard Form Ax + By = C • y = 0.7x + 1.3 • The 1st step is to multiply both sides by 10. You Try This One

  15. 2.) Writing an equation in Standard Form Ax + By = C • y = 0.7x + 1.3 • (10)y = (0.7x + 1.3)10 • 10y = 7x + 13 • 10y -7x = 7x -7x + 13 • -7x + 10y = 13

  16. Test 5 Review • Write Equations of lines given • a.)slope and y-intercept • b.) Graph of the line • c.) 2 points • d.) y=mx+b ~ Ax+By=C

  17. Test 5 Review • Do page 263 (1-9, skip 7) • Due Friday • Do Review worksheet

  18. Classwork • Do worksheet 5.6 • homework page 267 (1-18)

  19. Bellwork 12/3 ~ Write the equation of the line • 1.) (3,4) m = 6 • 2.) y-intercept = 3, slope=2 • 3.) (6,-2) & (-4, 4)

  20. Write the equation • 1.) (3,4) m = 6 • y - y1 = m(x - x1) • y - 4 = 6(x - 3) • y - 4 = 6x - 18 • y - 4 + 4 = 6x - 18 + 4 • y = 6x - 14

  21. Write the equation • 2.) y-intercept = 3, slope=2 • y = 2x + 3

  22. Write the equation • 3.) (6,-2) & (-4, 4) • m = (4 - -2)/(-4 - 6) • m = 6/-10 = - 3/5 • y - y1 = m(x - x1) • y - 4 = -3/5(x - -4)

  23. Write the equation • y - 4 = -3/5(x - -4) • y - 4 = -3/5x - 12/5 • y - 4 + 4= -3/5x - 12/5 + 4 • y = -3/5x + 8/5

  24. Test 5 Review • Write Equations of lines given • a.)slope and y-intercept • b.) Graph of the line • c.) 2 points • d.) y=mx+b ~ Ax+By=C

  25. Chapter 5 Review • 1.) Slope = 2, y-intercept = -7 • y = 2x - 7 • 2.) Slope = 2, y-intercept = -3 • D.) y = 2x - 3

  26. Chapter 5 Review 3.) Write an equation Y 5 X -7 y = -12/5x - 7

  27. Chapter 5 Review • 4.) (-2, 6) , slope = -4 • y - y1 = m(x - x1) • y - 6 = -4(x - -2) • y - 6 = -4x - 8 • y - 6 + 6 = -4x - 8 + 6 • y = -4x -2

  28. Chapter 5 Review • 5.)5y - 2x = 3 • 5y - 2x + 2x = 3 + 2x • 5y = 2x + 3 • 5y/5 = (2x + 3)/5 • y = 2/5x + 3/5

  29. Chapter 5 Review • 6.) (-5, -1) , slope = -4 • y - y1 = m(x - x1) • y - -1 = -4(x - -5) • y + 1 = -4x - 20 • y + 1 - 1 = -4x - 20 - 1 • y = -4x - 21

  30. Chapter 5 Review • 7.) (3,-1) , slope = 3 • y - y1 = m(x - x1) • y - -1 = 3(x - 3) • y + 1 = 3x - 9 • y + 1 - 1 = 3x - 9 - 1 • y = 3x - 10

  31. Chapter 5 Review 8.) (-2, -2) slope = 2 Y y = 2x + 2 X

  32. Chapter 5 Review • 9.)(2, -18) and ( 1,-12) • 1.) Find the Slope • m = (-12 - -18)/(1 - 2) • m = (-12 + 18)/(-1) • m = 6/-1 = -6

  33. Chapter 5 Review • 9.)(2, -18) and ( 1,-12) • y - y1 = m(x - x1) • y - -12 = -6(x - 1) • y + 12 = -6x + 6 • y + 12 - 12 = -6x + 6 - 12 • y = -6x - 6

  34. Chapter 5 Review 10.) Write an Equation Y y = -2/3x + 6 X

  35. Chapter 5 Review • 11.)y = -3/5x + 9/5 • (5)y = (-3/5x + 9/5)5 • 5y = -3x + 9 • 5y + 3x = -3x + 3x+ 9 • 3x + 5y = 9

  36. Chapter 5 Review • 12.)(2, -4) and ( 7,3) • 1.) Find the Slope • m = (3 - -4)/(7 - 2) • m = 7/5

  37. Chapter 5 Review • 12.)(2, -4) and ( 7,3) • y - y1 = m(x - x1) • y - -4 = 7/5(x - 2) • y + 4 = 7/5(x - 2)

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