Question 27578
STEP 1
          What is given?
             * line L with y-intercept (0,2)
             * line with equation 2x-3y=6 but perpendicular to line L
STEP 2
          Draw a diagram

STEP 3
          To find the equation of any line you need 2 things, namely, 
          gradient and a point on the line you want to find the equation of.
STEP 4
          The point on L is (0,2)
          The gradient we get from the line 2x-3y=6 since it is perpendicular 
          to L. What do we know about perpendicular lines? Yes, the product 
          of their gradients is -1.
          What is the gradient of 2x-3y=6? Write 2x-3y=6 in the y-form i.e 
          make y subject of the formula. Thus
                            2x-3y=6
                            -3y=6-2x
                              y=-2+(2/3)x
                 which means the gradient is 2/3.
STEP 5
          since the lines are perpendicular, the product of gradients is -1
                     (gradient L)(2/3)= -1  therefore 
                        gradient L = -3/2

Step 6            using the formula for a straight line y=mx+c
                  we substitute for m, which is the gradient L = -3/2
                  and c, which is the y-intercept 2 to get the required 
                  equation of L  y = (-3/2)x + 2