Standard Equation Form

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Standard form equation for the slope of a line

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Standard Equation Form

  1. 1. So Who’s Confused??
  2. 2. 1.) Write an equation of a line given <ul><li>The points (1,6) & (3,-4) </li></ul><ul><li>1.) Find the Slope </li></ul><ul><li>m = (-4 -6)/(3-1) </li></ul><ul><li>m = -10/2 = -5 </li></ul>
  3. 3. Write an equation of a line given <ul><li>The points (1,6) & (3,-4) </li></ul><ul><li>2.) Plug in one of the points (y - y 1 ) = m(x - x 1 ) </li></ul><ul><li>(y - 6 ) = -5 (x - 1 ) </li></ul><ul><li>y - 6 = -5x + 5 </li></ul>
  4. 4. Write an equation of a line given <ul><li>y - 6 = -5x + 5 </li></ul><ul><li>y - 6 + 6 = -5x + 5 + 6 </li></ul><ul><li>y = -5x + 11 </li></ul>
  5. 5. So which one is an equation of the line?? <ul><li>y - 6 = -5x + 5 </li></ul><ul><li>y = -5x + 11 </li></ul>
  6. 6. Today’s Objective <ul><li>To be able to Re-Write and equation in Standard Form. </li></ul><ul><li>Ax + By = C…… where </li></ul><ul><li>A,B & C are real numbers </li></ul>
  7. 7. Equations of Lines <ul><li>Vertical line x = # </li></ul><ul><li>Horizontal line y = # </li></ul><ul><li>Slope, y-intercept y=mx+b </li></ul><ul><li>Point, Slope y-y 1 =m(x-x 1 ) </li></ul><ul><li>Standard Form Ax+By = C </li></ul>
  8. 8. 1.) Writing an equation in Standard Form Ax + By = C <ul><li>y = 2/5x - 3 </li></ul><ul><li>The 1 st step is to multiply both sides by 5 . </li></ul>Why?
  9. 9. 1.) Writing an equation in Standard Form Ax + By = C <ul><li>y = 2/5x - 3 </li></ul><ul><li>(5) y = (2/5x - 3) 5 </li></ul><ul><li>5y = 2x - 15 </li></ul><ul><li>5y -2x = 2x -2x - 15 </li></ul><ul><li>-2x + 5y = -15 </li></ul>
  10. 10. Writing an equation in Standard Form Ax + By = C <ul><li>y = 1/2x + 4 </li></ul><ul><li>The 1 st step is to multiply both sides by 2 . </li></ul>You Try This One
  11. 11. Writing an equation in Standard Form Ax + By = C <ul><li>y = 1/2x + 4 </li></ul><ul><li>(2) y = (1/2x + 4) 2 </li></ul><ul><li>2y = x + 8 </li></ul><ul><li>2y -x = x -x + 8 </li></ul><ul><li>-x + 2y = 8 </li></ul>
  12. 12. 2.) Writing an equation in Standard Form Ax + By = C <ul><li>y = 0.55x + 1.35 </li></ul><ul><li>The 1 st step is to multiply both sides by 100 . </li></ul>Why?
  13. 13. 2.) Writing an equation in Standard Form Ax + By = C <ul><li>y = 0.55x + 1.35 </li></ul><ul><li>(100) y = (0.55x + 1.35) 100 </li></ul><ul><li>100y = 55x + 135 </li></ul><ul><li>100y -55x = 55x -55x + 135 </li></ul><ul><li>-55x + 100y = 135 </li></ul>
  14. 14. -55x + 100y = 135 <ul><li>Since all 3 TERMS are divisible by 5, we can simplify by dividing both sides by 5. </li></ul><ul><li>(-55x + 100y) /5 = 135 /5 </li></ul><ul><li>-11x + 20y = 27 </li></ul>
  15. 15. Writing an equation in Standard Form Ax + By = C <ul><li>y = 0.7x + 1.3 </li></ul><ul><li>The 1 st step is to multiply both sides by 10 . </li></ul>You Try This One
  16. 16. 2.) Writing an equation in Standard Form Ax + By = C <ul><li>y = 0.7x + 1.3 </li></ul><ul><li>(10) y = (0.7x + 1.3 ) 10 </li></ul><ul><li>10y = 7x + 13 </li></ul><ul><li>10y -7x = 7x -7x + 13 </li></ul><ul><li>-7x + 10y = 13 </li></ul>
  17. 17. Write the equation <ul><li>1.) (3,4) m = 6 </li></ul><ul><li>y - y 1 = m(x - x 1 ) </li></ul><ul><li>y - 4 = 6 (x - 3 ) </li></ul><ul><li>y - 4 = 6x - 18 </li></ul><ul><li>y - 4 + 4 = 6x - 18 + 4 </li></ul><ul><li>y = 6x - 14 </li></ul>
  18. 18. Write the equation <ul><li>2.) y-intercept = 3, slope=2 </li></ul><ul><li>y = 2x + 3 </li></ul>
  19. 19. Write the equation <ul><li>3.) (6,-2) & (-4, 4) </li></ul><ul><li>m = (4 - -2)/(-4 - 6) </li></ul><ul><li>m = 6/-10 = - 3/5 </li></ul><ul><li>y - y 1 = m(x - x 1 ) </li></ul><ul><li>y - 4 = -3/5 (x - -4 ) </li></ul>
  20. 20. Write the equation <ul><li>y - 4 = -3/5 (x - -4 ) </li></ul><ul><li>y - 4 = -3/5x - 12/5 </li></ul><ul><li>y - 4 + 4 = -3/5x - 12/5 + 4 </li></ul><ul><li>y = -3/5x + 8/5 </li></ul>

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