Chapter 0.1, Problem 50E

To determine

To find: Find the equation of line passing through $\left(-2,-1\right)$ parallel to the line $y=5-3\left(x+4\right)$ .

Answer to Problem 50E

The required equation of line is $y=-1-3\left(x+2\right)$ .

Explanation of Solution

Given information:

It is given that equation of parallel line is $y=5-3\left(x+4\right)$ and the point is $\left(-2,-1\right)$ .

Concept used: If two lines are parallel then their slope is equal.

Calculation:

Rewrite the give equation of line.

  $\begin{array}{l}y=5-3\left(x+4\right)\\ y=5-3x-12\\ y=-3x-7\end{array}$

Compare the equation (1) with general equation of line $y=mx+c$ .

The slope of the line is $-3$ .

Since both lines are parallel so slope of the other line will be $-3$ .

Now the equation of line which passes through the point $\left(x_1,y_1\right)$ and having slope $m$ is:

  $y-y_1=m\left(x-x_1\right)$

Substitute $x_1=-2,y_1=-1,m=-3$ .

  $\begin{array}{l}y-\left(-1\right)=-3\left(x-\left(-2\right)\right)\\ y+1=-3\left(x+2\right)\\ y+1=-3x-6\\ y=-1-3\left(x+2\right)\end{array}$

The required equation of line is $y=-1-3\left(x+2\right)$ .