Chapter G, Problem 1DE

To determine

To calculate: The equation of the line where the slope is $m=-3$ and contains the point $\left(-5,4\right)$.

Answer to Problem 1DE

Solution:

The equation of the line where the slope is $m=-3$ and contains the point $\left(-5,4\right)$ is $y=-3x-11$.

Explanation of Solution

Given Information:

The slope is $m=-3$ and the point is $\left(-5,4\right)$.

Formula used:

The point-slope equation of a line that has slope $m$ and passing point $\left(x_1,y_1\right)$ is denoted by the formula;

$y-y_1=m\left(x-x_1\right)$

Calculation:

Here, slope is $m=-3$ and the point is $\left(-5,4\right)$.

That is, $\left(x_1,y_1\right)=\left(-5,4\right)$.

As the point-slope equation of a line that has slope $m$ and passing point $\left(x_1,y_1\right)$ is denoted by the formula;

$y-y_1=m\left(x-x_1\right)$

Thus, it becomes;

$\begin{array}{c}y-4=-3\left(x-\left(-5\right)\right)\\ y-4=-3\left(x+5\right)\\ y-4=-3x-15\\ y=-3x-11\end{array}$

Hence, the equation of the line where the slope is $m=-3$ and contain the point $\left(-5,4\right)$ is $y=-3x-11$.