parallel, perpendicular straight line equation question

Question

Hi there, I have a straight line equation that i do not know how to solve, could you help me? the equation is like this:

Find the equation of the line that:
1. is perpendicular to the line y=3x-1
and
2. passes through the point (7,4).

 

Thanks

Answer 1

The slope of a perpendicular line is the negative reciprocal of the slope of the original line.  So in this case where the slope of the given line is 3, the slope of the perpendicular line is -1/3.  Once we have the slope, we can use the point-slope formula: m(X-x1) = Y-y1 to get -1/3(x-7) = y-4.  This can be rewritten as y = (-1/3)x + 19/3.