If the two lines are perpendicular then the products of thier slope is ( -1 )
The general form of equation of line :
[tex]y-y_1=m(x-x_1)[/tex]where, m = slope, (x1, y1) are the passing point
The given equation of line : 2x - 7y = -6
Simplify in the general form
[tex]\begin{gathered} 2x-7y=-6 \\ 2x+6=7y \\ 7y=2x+6 \\ y=\frac{2}{7}x+\frac{6}{7} \end{gathered}[/tex]On comparing with the general form of line, we get slope = 2/7
Let the slope of the perpendicular line is m
Thus, from the slope creteria of perpendicular line : m(2/7)=-1
[tex]\begin{gathered} m(\frac{2}{7})=-1 \\ m=\frac{-7}{2} \end{gathered}[/tex]Substitute the passing point(-2,6) and slope m = -7/2 in the equation of line.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-6=\frac{-7}{2}(x-(-2)) \\ y-6=\frac{-7}{2}(x\text{ +2)} \\ y-6=\frac{-7}{2}x-\frac{-14}{2} \\ y=-\frac{7}{2}x+7+6 \\ y=\frac{-7}{2}x+13 \\ 2y=-7x+26 \\ 7x+2y=26 \end{gathered}[/tex]Equation of perpendicular line is 7x + 2y = 26
Answer : 7x + 2y = 26
