perpendicular means the slopes of the two lines are opposite reciprocals. Since the slope of y = 3x + 1 is "3", then the opposite reciprocal slope is [tex] \frac{-1}{3} [/tex]
Next, plug in the slope ([tex] \frac{-1}{3} [/tex] )and point (1, -1) into the point-slope formula: y - y₁ = m(x - x₁); where (x₁, y₁) is the point.
y - (-1) = [tex] \frac{-1}{3} [/tex](x - 1)
y + 1 = [tex] \frac{-1}{3} [/tex]x + [tex] \frac{1}{3} [/tex]
y = [tex] \frac{-1}{3} [/tex]x + [tex] \frac{-2}{3} [/tex]
