Answer:
[tex]\sf y = \dfrac{-1}{13}x+ \dfrac{165}{13}[/tex]
Step-by-step explanation:
Here m is the slope and b is the y-intercept.
y = 13x - 4
m₁ = 13
Product of slope of the Perpendicular line m * m₁ = -1
[tex]\sf m = \dfrac{-1}{m_1}\\\\m = \dfrac{-1}{13}[/tex]
Equation of the line:
[tex]\sf y = \dfrac{-1}{13}x+b[/tex]
The point (9,12) passes through the line. Substitute the coordinates in the above equation and find the value of 'b'.
[tex]\sf 12 = \dfrac{-1}{13}*9+b\\\\[/tex]
[tex]\sf 12 + \dfrac{9}{13}=b\\\\ \dfrac{156}{13}+ \dfrac{9}{13}=b\\\\\boxed{b= \dfrac{165}{13}}[/tex]
Equation of line:
[tex]\sf y = \dfrac{-1}{13}x+ \dfrac{165}{13}[/tex]