Question

what is the slope of a line perpendicular to (5,7) and (10,3)

Answer 1

If you have two lines, for example:

$y=mx+b$

with slope "m"

and

$y=nx+c$

with slope "n"

That are perpendicular, the relationship between the slopes is that one is the inverse negative of the others, symbolically:

$n=-\frac{1}{m}$

So the first step is to use the known points of one of the lines to calculate the slope using the formula:

$m=\frac{y_1-y_2}{x_1-x_2}$

For (5,7) and (10,3)

$\begin{gathered} m=\frac{3-7}{10-5}=\frac{-4}{5} \\ m=-\frac{4}{5} \end{gathered}$

Now that you have determined the value of the slope, you can determine the slope of a line perpendicular to it as:

$\begin{gathered} n=-\frac{1}{m} \\ n=-(-\frac{5}{4}) \\ n=\frac{5}{4} \end{gathered}$

The slope of the perpendicular line to one that passes through points (5,7) and (10,3) is 5/4