Question

Points (3,1) and (1,4) lie on line k. What is the slope of the line that is perpendicular to k?

Answer 1

First we need to find the slope of line k.  Using the slope formula, we fill in accordingly: $m= \frac{4-1}{1-3}$.  The slope is -3/2.  The slope of a line that is perpendicular to line k will have the opposite sign (so, positive) and will be the reciprocal of the line k's slope (so, 2/3).  You could also say, more "mathematically legal", that the product of the slopes of perpendicular lines is -1, but it's easier to just say that they are opposite reciprocals.  The slope you're looking for is 2/3.  Choice 3 above.