Chapter 7.CT, Problem 1CT

To determine

To find:

The slope of the given line.

Answer to Problem 1CT

Solution:

The slope of the given line is $\frac{-6}{5}$.

Explanation of Solution

Given:

The points are $\left(-2,4\right)$ and $\left(3,-2\right)$.

Formula used:

The slope $m$ of a line determined by the 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, $x_2\ne x_1$.

Calculation:

Given points are $\left(-2,4\right)$ and $\left(3,-2\right)$.

Let the point $\left(-2,4\right)$ be $\left(x_1,y_1\right)$ and the point $\left(3,-2\right)$ be $\left(x_2,y_2\right)$.

Substitute $-2$ for $x_1$, $4$ for $y_1$, $3$ for $x_2$, and $-2$ for $y_2$ in the above mentioned formula,

$\begin{array}{rll}m& =& \frac{-2-4}{3-\left(-2\right)}\\ & =& \frac{-2-4}{3+2}\\ & =& \frac{-6}{5}\end{array}$

The slope of the given line is $\frac{-6}{5}$.

Conclusion:

Therefore, the slope of the given line is $\frac{-6}{5}$.