equation in point slope form

Question

Given the points (3, 3) and (0, -3), construct two equations in point slope form using each of the points. 

Answer 1

 

Point slope form of a line has the form  y-y_o = m(x - x_o)

Where  m = slope

         (x_o, y_o) = one of the two points

 

Let's assign  (x_o, y_o) = (0,-3)   (it doesn't matter which you choose)

 

Now calculate m by  m = (y₁ - y_o) /  (x₁-x_o)

                              m = (3 - (-3)) / (3 - 0) = 6/3 = 2

 

 So the equation for the line, in point-slope form is:  y - (-3) = 2(x - 0)

 Which may be cleaned up to:

                       y + 3 = 2x

 

Check:

              3 + 3 = 2(3) 

                    6 = 6    (ok)   So the equation agrees (3,3) is on the line

 

               -3 + 3 = 2(0)

                       0 = 0  (ok)   So the equation agrees (0,-3) is also on the line