A line m goes through the point (4, -3) and is perpendicular to the line 3x + 2y = 9. The point (k, k +3) lies on this perpendicular line m. Find the value of k

Question

 know there's a formula but I can't think of what

Answer 1

The equation of a first line is given in Standard Form (Ax+By=C):  3x + 2y = 9.

 

The line m is perpendicular to it; that means that line m has a slope that is the negative reciprocal of the slope of the first line.  The slope of the first line (-A/B) is -3/2 and slope of the perpendicular line m is 2/3.  This makes the equation line m:

     2x - 3y = D   and we need point (4,-3) to determine D.

       2(4) - 3(-3) = D

         8 + 9 = D

             17 = D

 

The equation of line m is 2x - 3y = 17

 

"The point (k,k+3) lies on this perpendicular line m.  Find the value of k."

      2(k) - 3(k+3) = 17

        2k -3k -9 = 17

           -k = 26

             k = -26

 

Let's check that (k,k+3) [that is, (-26,-23)] is on the perpendicular line m:

         2(-26) - 3(-23) = 17   ?

           -52 + 69 = 17   ?

                  17 = 17   ?yes