Finding the Equation of a Line Given 2 Points To find the equation of a line given 2 points, follow this 2 step process: Step 1:  Find the slope using the formula                     y2 - y1         m  =                                         x2 - x1 Step 2:  Find the equation of the line using the point-slope formula         y - y1  =  m(x - x1) Then multiply out, solve for y and simplify. Example 1 Find the equation of the line through the points (2,5) and (4,1) Solution Step 1:  We find                     1 - 5         m  =                                      4 - 2                     -4          =               =  -2                   2   Step 2:  Use the point-slope formula         y - 5  =  -2(x - 2) Multiply through to get         y - 5  =  -2x + 4 Now add 5 to both sides to get         y  =  -2x +9 Example 2 Find the equation of the line through the points (-3,4) and (-2,-5) Solution Step 1:  We find                     -5 - 4         m  =                                       -3 - 2                     -9             9          =               =                               -5             5   Step 2:  Use the point-slope formula         y - 4  =  9/5(x - (-3)) Multiply through to get         y - 4  =  9/5 x + 27/5 Now add 4 to both sides to get         y  =   9/5 x + 27/5 + 4 we need to add the fractions:         27        4               +                       5         1           27        20     =          +                         5         5           47       =                        5 We now have the equation of he line:     y  =   9/5 x + 47/5 e-mail Questions and Suggestions