Chapter 13, Problem 7CT

To determine

To write an equation of the line through $(-2,\text{ 5})$ and parallel to $3x+y=6$

Answer to Problem 7CT

The equation of the line is $3x+y=-1$

Explanation of Solution

Given information :

The line through $(-2,\text{ 5})$ and parallel to $3x+y=6$

  $\begin{array}{l}3x+y=6\\ y=-3x+6\end{array}$

Slope of the given line, $m_1=-3$

The general equation of the line parallel to the $y=-3x+6$ is,

  $y=m_{2}x+c$

Slope of this line, $m_2=m_1=-3$

The equation of the line: $y=-3x+c$

The line passes through $(-2,\text{ 5})$

Therefore,

  $\begin{array}{l}y=-3x+6\\ 5=-3\cdot (-2)+c\\ 5=6+c\\ c=-1\end{array}$

Now, the equation of the line,

  $\begin{array}{l}y=-3x+(-1)\\ y=-3x-1\\ 3x+y=-1\end{array}$

Hence,

The equation of the line is $3x+y=-1$ .