Answer:[tex]y = - \frac{1}{3}x - 1[/tex]Step-by-step explanation:We have to write an equation of a line which passes through the given point (-9,2) and is perpendicular to the given straight line y = 3x - 12 ........... (1)
Now, equation (1) is in the slope-intercept form and the slope of the line is 3.
Let, m is the slope of the required line.
So, 3m = -1
{Since, the product of the slopes of two perpendicular straight lines is -1}
⇒ [tex]m = - \frac{1}{3}[/tex]
Therefore, the equation of the required line in slope intercept form is [tex]y = - \frac{1}{3} x + c[/tex] {Where c is a constant}
Now, this above equation passes through the point (-9,2) point.
So, [tex]2 = - \frac{1}{3} \times (-9) + c[/tex]
⇒ 2 = 3 + c
⇒ c = - 1 Therefore, the equation of the required straight line is [tex]y = - \frac{1}{3}x - 1[/tex] (Answer)