[tex]\Large\underline{\rm Solution :- }[/tex]
The given equation of the line is ,
[tex]\implies -3x - 9y = -45 \\\\\implies 3(x +3y) = 45 \\\\\implies x + 3y = 15 [/tex]
Convert it into Slope Intercept Form .
[tex]\implies y =\dfrac{-x}{3}+5[/tex]
We know that the product of slope of two perpendicular lines is -1. Therefore ,
[tex]\implies m_{(perp)}=3 [/tex]
On using Point - slope form of the line ,
[tex]\implies y - y_1 = m(x- x_1) \\\\\implies y - (-5) = 3( x - 7) \\\\\implies y + 5 = 3x - 21 \\\\\implies 3x - y -21 -5 = 0 \\\\\implies\underline{\boxed{ 3x - y - 26 =0}}[/tex]
