A line that is perpendicular to the graph of 3x+2y=6 and contains the point (6,-3)

y = (-2/3)x +1

Step-by-step explanation:

The standard equation of a line is: y=mx+b where m-is the slope, and b-is the y intercept. Rewrite the given equation in standard form.

3x+2y = 6

     2y = 3x+6

        y= (3/2)x+3

So the given equation has the slope m =3/2 and y-intercept= 3

A line ⊥ to the given line will have the slope negative reciprocal so the line is

        y= (-2/3 )x +b

To find b will substitute the given point (6,-3) in the new found equation

       -3= (-2/3 )6 +b

       -3= -4 +b

  -3+4 = b

        1 = b

The equation of the line that is perpendicular to the graph of 3x+2y=6 and contains the point (6,-3) is y = (-2/3)x +1