Question

How do you find the slope of the line passing through the points $\left(-3,4\right)$ and $\left(2,-1\right)$?

Answer 1

Finding the slope of the line passing through two given points:

The slope of the line passes through two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is given by, $m=\frac{y_2-y_1}{x_2-x_1}$.

Where, $m$ is the slope and $x_1,x_2,y_1,\mathrm{and}{y}_2$ are arbitrary points.

Here,

$\begin{array}{rcl}{x}_1& =& -3\\ x_2& =& 2\\ y_1& =& 4\\ y_2& =& -1\end{array}$

Substitute the points in the slope formula,$m=\frac{y_2-y_1}{x_2-x_1}$:

$\begin{array}{rcl}m& =& \frac{-1-4}{2-\left(-3\right)}\\ & \Rightarrow & m=\frac{-5}{5}\\ & \Rightarrow & m=-1\end{array}$

Therefore, the slope of the line passes through $\mathbf{(}\mathbf{-}\mathbf{3}\mathbf{,}\mathbf{4}\mathbf{)}$ and $\mathbf{(}\mathbf{2}\mathbf{,}\mathbf{-}\mathbf{1}\mathbf{)}$ is $\mathbf{-}\mathbf{1}$.