The slope of the line passing through the points (0,0) and (2,3) is a.2/3 b.3/2 c.-3/2

The Standard Form of the equation of a line is Ax+By=C.

The problem gives two points which are on this line -->   (2,2) and (0,-3).

     A(2)+B(2)  =C

     A(0)+B(-3) =C

       [subtract equations]

      2A  + 5B    = 0

     2A = -5B              [choose A=5, B=-2]

The equation is:    5x - 2y = C         [use either point to find C]

      5(0) - 2(-3) = C

              6 = C

In Standard Format, the equation is:    5x -2y = 6

Check:

   Is   5(2) -2(2) = 6   ?

          10-4 = 6   ?

             6 = 6   >yes

   Is 5(0) -2(-3) = 6   ?

               6 = 6   ?yes