Work out the equation of the perpendicular bisector of $P(3,-1)$ and $Q(5,7)$
Give your answer in the form $y=a x+b$

Step 1 ：Find the midpoint of PQ using the midpoint formula: $M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$. P = (3, -1) and Q = (5, 7).

Step 2 ：Calculate the midpoint: $M = (\frac{3 + 5}{2}, \frac{-1 + 7}{2}) = (4.0, 3.0)$

Step 3 ：Find the slope of the line PQ using the slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Step 4 ：Calculate the slope: $m = \frac{7 - (-1)}{5 - 3} = 4.0$

Step 5 ：Find the slope of the line perpendicular to PQ: $m_{perp} = -\frac{1}{m}$

Step 6 ：Calculate the perpendicular slope: $m_{perp} = -\frac{1}{4.0} = -0.25$

Step 7 ：Use the point-slope form to find the equation of the perpendicular bisector: $y - y_1 = m_{perp}(x - x_1)$

Step 8 ：Substitute the midpoint and perpendicular slope into the equation: $y - 3.0 = -0.25(x - 4.0)$

Step 9 ：Simplify the equation to get the final answer: $y = \boxed{-0.25x + 4}$