The line that is perpendicular to y = 1/3x - 8 would have the negative reciprocal as the slope. So this means that the equation for the perpendicular line would be y = -3x + b. To find b, you can replace x and y with the coordinates from the point given (-1, 4). The equation would be 4 = -3(-1) +b. After solving this, you get 4 = 3 + b. Subtract 3 from both sides to isolate b, and you will get b = 1. When you plug this into the original equation, you get
y = -3x + 1. When put in standard form, you get 3x + y = 1.
