Verified Answer :
-3/x -4
Work:
turn 2x -3y = 13 to 2/3x -13/3.
flip 2/3x to 3/2x and change the positive sign to a negative
y = -3/2x
plug -6 into x and 5 into y
you get 5= 9
then subtract 4 from 9 to get 5 = 5.
Answer: The require equation of the line is \(3x+2y+8=0.\)
Step-by-step explanation: We are given to find the equation of the line perpendicular to the following line that passes through the point (–6, 5) :
\(2x-3y=13~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\)
We know that
the equation of a line in slope-intercept form is given by
\(y=mx+c,\)
where m is the slope of the line.
From equation (i), we have
\(2x-3y=13\\\\\Rightarrow 3y=2x-13\\\\\Rightarrow y=\dfrac{2}{3}x-\dfrac{13}{3}.\)
So, the slope of the line (i) is
\(m=\dfrac{2}{3}.\)
Let m' be the slope of the line that is perpendicular to line (i).
Since the product of the slopes of two perpendicular lines is -1, so we must have
\(m\times m'=-1\\\\\Rightarrow \dfrac{2}{3}\times m'=-1\\\\\Rightarrow m'=-\dfrac{3}{2}.\)
Since the line passes through the point (-6, 5), so its equation will be
\(y-5=m'(x-(-6))\\\\\\\Rightarrow y-5=-\dfrac{3}{2}(x+6)\\\\\Rightarrow 2y-10=-3x-18\\\\\Rightarrow 3x+2y+8=0.\)
Thus, the required equation of the line is \(3x+2y+8=0.\)