Chapter 1, Problem 34RE

To determine

To find: an equation of the line

Answer to Problem 34RE

The equation of the line is $x+y=-2$

Explanation of Solution

Given:

Parallel to the line $x+y=2$

point (1,-3)

Calculation:

The line is parallel to the line $x+y=2,$ that is $y=-x+2,$ thus the slope is $m=-1$

Equation of the line in point-slope form:

  $y-y_1=m\left(x-x_1\right),$

Where $m$ is the slope and $\left(x_1,y_1\right)$ is a point of the line

An equation of the line with slope -1 and containing the point (1,-3) can be found by usingthe point-slope form with $m=-1,x_1=1$ and $y_1=-3$

  $\begin{array}{c}\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-(-3)=-1(x-1)\end{array}\\ y+3=-x+1\\ \begin{array}{l}y=-x-2\\ x+y=-2\end{array}\end{array}$

Conclusion:

Therefore, the equation of the line is $x+y=-2$ .