Question

and the diagram PT St find the slope of st

Answer 1

You know that the lines PT and ST are perpendicular.

By definition, the slopes perpendicular lines are opposite reciprocal. This means that if the slope of a line is:

$m_1=a$

The slope of a perpendicular line to that line is:

$m_2=-\frac{1}{a}$

Knowing that:

$\begin{gathered} P\mleft(2,2\mright) \\ T\mleft(-1,-4\mright) \end{gathered}$

You can find the slope of the line PT using this formula:

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

Where two points on the line are:

$\begin{gathered} (x_1,y_1) \\ (x_2,y_2) \end{gathered}$

In this case, you can set up that for the line PT:

$\begin{gathered} y_2=-4_{} \\ y_1=2 \\ \\ x_2=-1 \\ x_1=2 \end{gathered}$

Then, substituting values into the formula and evaluating, you get:

$m_{PT}=\frac{-4-2}{-1-2}=\frac{-6}{-3}=2$

Knowing the slope of PT, you can determine that the slope of ST is:

$m_{ST}=-\frac{1}{2}$

Hence, the answer is:

$m_{ST}=-\frac{1}{2}$