Answer :
the general equation of a graph is y= mx + c
m is the gradient and c is the intercept
from the first line equation, m = 1/3
condition for perpendicularity is that if two lines are perpendicular
the gradient of the first line is equal to the negative of the reciprocal of the second line gradient
so
[tex]\begin{gathered} \text{if m}_{1\text{ }}is\text{ the gradient of the first line and } \\ m_{2\text{ }}is\text{ the gradient of the second line} \end{gathered}[/tex][tex]\frac{-1}{m_2}=m_1[/tex][tex]\begin{gathered} m_1=\text{ }\frac{1}{3},\text{ then } \\ m_2=\text{ -}\frac{\frac{1}{1}}{3}\text{ =- }\frac{1}{1}\times\frac{3}{1}=-3 \end{gathered}[/tex][tex]\begin{gathered} \text{if it passes through the points (-1,-2)} \\ x\text{ = -1, y=-2} \\ \text{use y= mx +c to obtain the value of c by substituting m, x and y} \end{gathered}[/tex][tex]\begin{gathered} y=mx\text{ + c} \\ -2\text{ = -3 }\times-1\text{ +c} \\ -2\text{ = 3 + c} \\ -2-3\text{ =c} \\ -5\text{ =c} \\ c=\text{ -5} \end{gathered}[/tex]so the equation of the line is obtain by substituting the values of the gradient (m2) and the intercept (c) in y = mx +c
so the equation is y = -3x + (-5)
y = -3x -5