Here is my problem: Find the equation of the normal line to the parabola $$y = x^2 - 5x + 4$$ that is parallel to the line $x - 3y = 5.$
I found the slope for the line to be $m = 1/3$. I found the derivative of the parabola to be $2x - 5$. I tried equating $2x - 5 = 1/3$ but I dont know if Im heading in the right direction.
You are heading in the right direction. Continue resolving $2x - 5 = \frac{1}{3}$, where you will find the $x$ point of the line. Then find the $y$ point and use the formula $y - y_1 = m(x - x_1)$, being the point you found $(x_1,y_1)$.