Given :
A Straight line passes through A(-2,1) and B(2,-k).
The line is perpendicular to a line 3y+2x=5 .
To Find :
The value of k.
Solution :
Let, slope of line is m.
We know, product of slope of in straight line is -1.
[tex]m \times \dfrac{-2}{3} = -1\\\\m = \dfrac{3}{2}[/tex]
We know, slope is given by :
[tex]\dfrac{y_2-y_1}{x_2-x_1} = \dfrac{3}{2}\\\\\dfrac{1-(-k)}{-2 - 2} = \dfrac{3}{2}\\\\\dfrac{1+k}{-4} = \dfrac{3}{2}\\\\k = -7[/tex]
Therefore, the value of k is -7.
