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Finding the equation of a line.

Finding the equation of a line. POINT-SLOPE FORM y – y1 = m ( x – x1 ). Bell Work. Using the point-slope form, find the equation of the line with the given conditions. Express your answer in y=mx + b. Having a slope of 3 and passing through the point ( 4, 5 ).

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Finding the equation of a line.

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  1. Finding the equation of a line. POINT-SLOPE FORM y – y1 = m ( x – x1 )

  2. Bell Work Using the point-slope form, find the equation of the line with the given conditions. Express your answer in y=mx + b. • Having a slope of 3 and passing through the point ( 4, 5 ). • Having a slope of -2 and passing through the point ( - 1, 6 ) • m = 8 , ( 7, 4 ) • m = -10 , ( 6, -8 ) • m = 5 , ( 9 , 3 )

  3. Take Note • If the given is the slope and a point on the line, we can use the point-slope form which is. • y – y1 = m ( x – x1 )

  4. What if the given slope is a fraction? • Try this! Find the equation of the line having a slope of ¾ and passing through ( 2, 5 ).

  5. Solution Given : m = ¾ and passing through ( 2,5 ) y – y1 = m ( x – x1 ) y – 5 = ¾ ( x – 2 ) y – 5 = ¾ x – 6/4 y = ¾ x – 6/4 + 5 y = ¾ x + 7/2

  6. Another solution m = ¾ and passing through ( 2, 5 ) y – y1 = m ( x – x1 ) y – 5 = ¾ ( x – 2 ) 4 ( y – 5 ) = 3 ( x – 2 ) 4y – 20 = 3x – 6 4y = 3x – 6 + 20 4y = 3x + 14 4 4 4 y = ¾ x + 7/ 2

  7. Try this! Find the equation of the line having the slope of ½ and passing through ( - 3, 4 )

  8. Try this! Find the equation of the line having a slope of 2/5 and passing through ( - 3, - 6 )

  9. Try this! Find the equation of the line having a slope of -2/7 and passing through ( - 1, - 4 )

  10. Think – Pair - Share Find the equation of the line given the slope and a point. • m = 2/3 ( 4, 7 ) • m = ¼ ( 3, 1) • m = 3/5 ( -2, 4) • m = - 1/8 ( 3, -2) • m = ½ ( 0, -23 )

  11. Finding Slopes and y - intercepts from Equations y = mx + b

  12. Objectives: • Change a linear equation to the form y = mx + b. • Determine the slope of a line and the y-intercept from the given equations.

  13. Thoughts to Ponder • To determine the slope and y – intercept from a given equation, solve the equation for y in terms of x and express the resulting equation in the form y = mx + b. The coefficient of the x-term is the slope (m) and the constant term b represents the y-intercept.

  14. Example: • Find the slope of the line and y-intercept of 8x + y = 10. Solution: Given: 8x + y = 10 y = mx + b y = -8x + 10 Therefore the slope is -8 and the y-intercept is 10.

  15. Example Find the slope and y-intercept in the line 2x + 2y = 12 Solution: 2x + 2y = 12 2y = -2x + 12 2 2 2 y = -x + 6 Slope = -1 : y-intercept = 6

  16. Try this! Change 3y + 15 = 3x in y-form.

  17. Try this! Change 2y + 6x = 30 in y-form.

  18. Board Drill • Change the following equations in the form y = mx + b. 10 x + y = 3

  19. 2x – 2y = 6

  20. 10x + 5y = 25

  21. 14 x- 7y = -12

  22. 2y – 4 = 35 – x

  23. Seatwork Change the following equations in the form y = mx + b, then determine the slope and y-intercept.

  24. Standard Form of Linear Equations Ax + By = C

  25. Mathematical Concepts • Standard Form Ax + By = C • This is one of the two forms of a linear equation. The letters A, B, and C represent numbers. The numbers may not be fractions.

  26. Examples • Change the equation y = -2x + 5 in Standard Form Given: y = -2x + 5 Solution: Just put all the variable terms on the left side of the equation. Note: x – term must comes first Answer: 2x + y = 5

  27. Examples 2. Change the equation y = 3x - 8 in Standard Form Given: y = 3x - 8 Solution: Just put all the variable terms on the left side of the equation. Note: the value of a should always be positive -3x + y = -8 -3x + y = -8 Multiply by -1 3x – y = 8

  28. Examples 3. Change the equation y = -2/3x - 7 in Standard Form Given: y = -2/3 x - 7 Solution: Just put all the variable terms on the left side of the equation. Note: there must be no fractions in A, B, or C 2/3 x + y = -7 2/3 x + y = -7 Multiply by 3 2x + 3y = -21

  29. Board Drill Write the following in standard form. y = 6x - 9

  30. Board Drill Write the following in standard form. 3x – 5 = 2y

  31. Board Drill Write the following in standard form. 7 = 2x – 3y

  32. Board Drill Write the following in standard form. y = -3/4x -10

  33. Board Drill Write the following in standard form. y = ½ x -7

  34. Seatwork Write the following equations in standard form. • y = -8x + 5 • y = 10x + 2 • 3x – 6 = 7y • y = 1/3 x – 5 • y = -4/9 x + 3

  35. Drills

  36. Drills

  37. Drills

  38. Did you know that?...... Using the Standard Form of Linear Equation we can also determine the value of the slope and y-intercept using the formula. SLOPE = Y-INTERCEPT =

  39. Change the equation in standard form then find the values of a, b, and c 3x = 5y + 2 S. F 3x – 5y = 2 A = 3 B = -5 C = 2

  40. Change the equation in standard form then find the values of a, b, and c y = 3x – 7 -3x + y = -7 Multiply by -1 3x – y = 7 Therefore: A = 3 B = -1 C = 7

  41. Change the equation in standard form then find the values of a, b, and c 3/4x = y – 7 ¾ x – y = -7 4 ( ¾ x – y = -7) 3x – 4y = -28 Therefore: A = 3 B = -4 C = -28

  42. Think-Pair-Share Complete the table below.

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