In the xy-coordinate plane, lines m and n are
perpendicular. If line m contains the points (0,0)
and (3, 1), and line n contains the points (2, 3) and
(1, a), what is the value of a?

A = 6

I found the slope of line m using slope formula (y2-y1 / x2-x1).

Line M slope is (1/3).

Perpendicular lines have a negative reciprocal slope. So we know line N slope will be -3.

Use slope formula again for line n with the line n coordinates given, AND equal it to -3 to solve for a.

Check out the pic to see work.