Question

Complete the point-slope equation of the line through (1,3) and (5,1)

Answer 1

First, solve for slope.
Formula for slope: $\frac{y2-y1}{x2-x1}$
Plug in values: $\frac{1-3}{5-1}= -\frac{2}{4} = -\frac{1}{2}$
Slope: $- \frac{1}{2}$
Second, we must plug into point-slope form. 
Formula for point-slope: $y - y1 = m(x-x1)$
Plug in the values: $y - 3 = - \frac{1}{2}(x-1)$

And there you have your answer in point-slope form.