Chapter 11.3, Problem 61STP

To determine

The equation of the line that passes through $\left(5,-8\right)$ and is parallel to the given line.

Answer to Problem 61STP

  $Gy+2x=2$

Explanation of Solution

Given:

The graph of the line

  

Calculation:

Observe that the given line passes through the points, $\left(-1,1\right),\text{ and }\left(0,-1\right)$ . So, the slope of the given line is

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{-1-1}{0-\left(-1\right)}\\ =\frac{-2}{1}\\ =-2\end{array}$

Now, since the slope of the parallel lines be equal, so the slope of the required line would be $m=-2$ as well.

So, the equation of the line passing through $\left(5,-8\right)$ and having slope $m=-2$ is given by

  $\begin{array}{c}y-y_1=m\left(x-x_1\right)\\ y-\left(-8\right)=-2\left(x-5\right)\\ y+8=-2x+10\\ y=-2x+10-8\\ y=-2x+2\\ y+2x=2\end{array}$

Thus, the equation of the required line is $y+2x=2$ .