Slope-intercept Equation of a Line using two points

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Since we have already discussed the slope intercept form of the equation of a line.

Slope-intercept Equation of a Line using two points

Substituting the value of m from above equation we have(y – y_{{1}}) =  \frac{(y_{{2}}-y_{1})}{(x_{{2}}-x_{1})} (x_{{}} – x_{{1}}),

which can be written as y=  \frac{(y_{{2}}-y_{1})}{(x_{{2}}-x_{1})}(x-x_{{1}})+y_{{1}}

Slope-intercept Equation of a Line using two points
Slope-intercept Equation of a Line using two points

Example

  1.  Find the equation of line passing through (2, 1) and (7, 2).Here slope m=  \frac{(y_{{2}}-y_{1})}{(x_{{2}}-x_{1})} = \left ( \frac{(2_{{}}-1_{})}{(7_{{}}-1_{})}\right )=\frac{1}{5}Substitute the value of m from above we have(y-5)=\frac{1}{5}(x-2)or y=\frac{1}{5}x−\frac{2}{5}+1=\frac{1}{5}x+\frac{3}{5} which is the slope intercept form obtained using two points.
  2. Find the equation of line passing through (3, 0) and (5, 8).Here slope m= \frac{(y_{{2}}-y_{1})}{(x_{{2}}-x_{1})} = \left ( \frac{8_{{}}-0_{}}{5_{{}}-3_{}} \right )\frac{8}{2} = 4Substitute the value of m from above we have (y – 0) = 4(x – 3) = 4x – 12or y = 4x – 12.                                      

CHECK POINT

 

  1. Find the equation of a line passing through (5, 3) & (-5, -3).
  2. Find the equation of a line passing through (2, 4) & (0, 6) in slope intercept form.
  3. Find the equation of a line passing through (15, 9) & (9, 15) in slope intercept form.
  4. Find the equation of a line passing through (0, 3) & (11, -7) in slope intercept form.
  5. Find the equation of a line passing through (0, 0) & (12, 23) in slope intercept form.
Answer key
  1. 3x – 5y = 0 or y \frac{3}{5}x
  2. Y = (-x + 6)
  3. y = 24 –x
  4. y =\frac{-10}{11}x + 3
  5. y \frac{23}{12}x