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=-(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=(y_1-y_2)/(x_1-x_2)`

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

`\begin{gathered} m=(3-7)/(10-5)=(-4)/(5) \\ m=-(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=-(1)/(m) \\ n=-(-(5)/(4)) \\ n=(5)/(4) \end{gathered}`

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