Chapter 8, Problem 19CR

To determine

To write:

An equation of the line that is parallel to the given line and passes through

  $\left(0,-6\right)$ .

Answer to Problem 19CR

The equation of parallel line to our given line would be $y=-x-6$ .

Explanation of Solution

Given:

An equation:

  $y=-x$ .

Concept used:

We know that the slopes of two parallel lines are same.

The equation of a line in slope-intercept form is $y=mx+b$ , where m represents slope of line and b represents the y-intercept.

Calculation:

We can see from our given equation that it is in slope-intercept form and its slope is $-1$ . So, the slope of parallel line to our given line will be $-1$ .

Now we will substitute the slope and y-intercept $\left(0,-6\right)$ in slope-intercept form of equation as:

  $\begin{array}{l}y=mx+b\left(\text{Slope-intercept form of equation}\right)\\ y=-1\cdot x+(-6)\left(\text{Substituting }m=-1\text{ and }b=-6\right)\\ y=-x-6\end{array}$

Therefore, the equation of parallel line to our given line is $y=-x-6$ .