Answer:
C
Step-by-step explanation:
(1) -7x - 8y = 12 ⇔ -8y = 7x + 12 ⇔ y = [tex]\frac{-7x}{8} - \frac{12}{8} = \frac{-7x}{8} - \frac{3}{2}[/tex]
The two lines that are perpendicular as [tex]x_{1} * x_{2} = -1[/tex]
So, the slope of the second equation is: [tex]x_{2} = 1/ \frac{-7}{8} = \frac{8}{7}[/tex]
Thus, we have: [tex]y_{2} = \frac{8}{7} x + b[/tex] (2)
Plug P(-3,1) into (2): 1 = [tex]\frac{8}{7} * (-3) + b[/tex] ⇒ b = [tex]\frac{31}{7}[/tex]
Therefore, the result will be C. y = [tex]\frac{8}{7}[/tex]*x + [tex]\frac{31}{7}[/tex]
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