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Write the Equation of a Line Using the Point/Slope Formula

Write the Equation of a Line Using the Point/Slope Formula. Equations of a line: y = mx +b slope-intercept form or Ax + By = C standard form. The Point-Slope Formula.

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Write the Equation of a Line Using the Point/Slope Formula

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  1. Write the Equation of a LineUsing the Point/Slope Formula Equations of a line: y = mx +b slope-intercept form or Ax + By = Cstandard form

  2. The Point-Slope Formula To use this formula and get the equation to represent a line you must know the slope (m) and a point (x1, y1). Plug them in!! y - y1 = m ( x - x1)

  3. (-3,1) Write the Equation of a line: Ex: Given the point (-3, 1) and the slope ½, write the equation of the line. First it is good to have a vision of this line. Draw a sketch. m = ½ Now write a name or an equation for this line.

  4. Write the Equation of a line: Ex: Given the point (-3, 1) and the slope ½, write the equation of the line. (-3, 1) = (x1, y1) Slope: m =½ Plug these values into the formula. y - y1 = m ( x - x1) ½ -3 1

  5. Write the Equation of a line: Now that you have an equation (= sign in the algebra sentence) , write it into the form you want. y - -3 = ½ ( x - 1) y = mx +b slope-intercept form? or Ax + By = Cstandard form?

  6. EQ of line in slope-intercept Write the Equation of the line in Slope-Intercept form. y = mx +b y - 3 = ½ ( x - 1) 1st: Distribute 2nd : get y= y - 3 = ½x - ½ y = ½x +2½ Check: Is (-1, 3) a solution to the equation? Is slope =½?

  7. Check: Is (-1, 3) a solution to the equation? EQ of line in standard form Write the Equation of the line in Standard Form. Ax + By = C y - 3=½ ( x - 1) 1st: Mult. EQ by 2 2(y – 3)=2·½ ( x - 1) 2nd : Distribute 2y - 6 =x - 1 3rd : Get x & y on same side of = -x +2y =5 4th : Clear fractions & make “A” positive x - 2y = -5

  8. -2 - 2 4 - -1 = = - 4 5 Write the Equation of a line: Ex: Write the equation of the line passing through the point (4, -2) and the point (-1, 2). First find the slope: Now that you know the slope, use this slope and either one of the points to write an equation.

  9. EQ of line in slope-intercept Write the Equation of the line (4, -2) = (x1, y1) Slope: m =-4/5Plug these values into the formula. y - -2 = -4/5( x - 4) 1st: Distribute 2nd : get y= y + 2 = -4/5 x +16/5 y = -4/5 x +11/5 Check: Is (-1, 2) a solution to the equation? AND Is (4, -2) a solution to the equation?

  10. Watch your signs! EQ of line Write the Equation of the line: Write the equation of a line going through the point (-2, -3) with a slope of -5. y - y1 = m ( x - x1) y – -3 = -5(x – -2) y + 3 = -5x - 10 y = -5x - 13

  11. The End

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