Equation Of A Line

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Equation Of A Line

  1. 1. Equation of a Line <ul><li>1. Slope and y -intercept </li></ul><ul><li>2. Graph </li></ul><ul><li>3. Slope and one point </li></ul><ul><li>4. Two points </li></ul><ul><li>5 . x - and y -intercepts </li></ul>
  2. 2. <ul><li>Find the Equation of the Line Given the Slope and y -intercept </li></ul><ul><li>m = -3, b = 1 </li></ul><ul><li>m = -2, b = -4 </li></ul><ul><li>m = 0, b = 10 </li></ul><ul><li>m = 1, b = 0 </li></ul><ul><li>m = 0, b = 0 </li></ul><ul><li>Substitute m and b into y = mx + b </li></ul>y = -3 x + 1 y = -2 x - 4 y = 0 x + 10, y = 10 y = 1 x + 0, y = x y = 0 x + 0, y = 0
  3. 3. <ul><li>Find the Equation of a Line Given the Graph </li></ul><ul><li>Find the y -intercept from the graph. </li></ul><ul><li>Count the slope from the graph. </li></ul>
  4. 4. Example 1 <ul><li>b = -3 </li></ul><ul><li>m = </li></ul><ul><li>y = x - 3 </li></ul>x y
  5. 5. Example 2 <ul><li>b = 1 </li></ul><ul><li>m = </li></ul><ul><li>y = x + 1 </li></ul>x y +1 -2
  6. 6. Example 3 <ul><li>b = 4 </li></ul><ul><li>m = 0/1= 0 </li></ul><ul><li>y = 0 x + 4, y = 4 </li></ul>x y
  7. 7. Example 4 <ul><li>x = 2 </li></ul>x y
  8. 8. Dude! You try one.
  9. 9. y = x + 2 x y
  10. 10. <ul><li>Find the Equation of a Line Given the Point and the Slope </li></ul><ul><li>Use the Point-Slope Formula: </li></ul><ul><li>is the given point </li></ul><ul><li>Substitute m and into the formula </li></ul>
  11. 11. Example 1 <ul><li>Write the equation of the line with slope = -2 and passing through the point ( 3 , -5 ). </li></ul>y – (-5) = -2 ( x – 3 ) y + 5 = -2x + 6 y = -2x + 1
  12. 12. Remember this! Parallel lines have the same slope . m = m Perpendicular lines have a slope which is a negative reciprocal of the other. m = - ( 1/m )
  13. 13. Example 2 Find the equation of a line passing through ( 4,2 ) and parallel to y = 3x + 7. m = 3 x 1 = 4 ; y 1 = 2 y – 2 = 3 (x - 4) y – 2 = 3x - 12 y = 3x -10
  14. 14. Example 3 Find the equation of a line passing through ( 6,-3 ) and m = 3 perpendicular to y = 3x + 7. m = - 1/3 x 1 = 6 ; y 1 = -3 y – (-3) = -1/3 ( x – 6 ) y + 3 = -1/3 x + 2 y = - 1/3 x - 1
  15. 15. Seat work: ( ½ crosswise ) <ul><li>Answer page 98. </li></ul><ul><li>#’s 25, 34, 37 and 40 </li></ul>
  16. 16. Homework: (1/2 crosswise) <ul><li>Answer page 98. </li></ul><ul><li>#’s 26, 35, 38 and 41. </li></ul>
  17. 17. <ul><li>Find the Equation of the Line Given Two Points </li></ul><ul><li>Calculate the slope of the two points. </li></ul><ul><li>Use one of the points and the slope to substitute into the Point-Slope formula. </li></ul>
  18. 18. Example <ul><li>Write the equation of the line that goes through the points (3, 2) and (5, 4). </li></ul>m = 2/2 or 1 y – 2 = 1 ( x -3 ) y – 2 = x -3 y = x - 1
  19. 19. Equation of a Line in diff. forms <ul><li>Slope – intercept form: y = mx + b </li></ul>y = x -1 Standard form : Ax + By = C x – y = 1 General form: Ax + By + C = 0 x – y – 1 = 0
  20. 20. Try this! <ul><li>Write the equation of the line that goes through the points (5, 2) and (-3, 7). </li></ul>
  21. 21. <ul><li>Find the Equation of the Line Given the x - and y - intercepts </li></ul><ul><li>Write the intercepts as ordered pairs. </li></ul><ul><li>The x -intercept 4 is the ordered pair (4, 0). </li></ul><ul><li>The y -intercept -2 is the ordered pair (0, -2). </li></ul><ul><li>Calculate the slope. </li></ul><ul><li>Substitute the slope and the y -intercept ( b ) into the slope-intercept formula. </li></ul>
  22. 22. Example <ul><li>Write the equation of the line with x -intercept 3 </li></ul><ul><li>and y -intercept 2. </li></ul><ul><li>x -intercept 3 = (3, 0); y -intercept 2 = (0, 2) </li></ul><ul><li>Slope: </li></ul>y = mx + b
  23. 23. Seatwork: (1/2 crosswise) <ul><li>Express your answer in different forms of equation. (slope-intercept , standard and general) </li></ul><ul><li>1.Find the equation of a line which goes through (1,-3) and (-5,2). </li></ul><ul><li>2. Find the equation of a line with x-intercept of 4 and y-intercept of -16. </li></ul>

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