Chapter 8.6, Problem 19E

To determine

To find:

The equation of the line that is parallel to the given line and passes through $\left(0,7\right)$ .

Answer to Problem 19E

The equation of parallel lineto our given line is $y=-x+7$ .

Explanation of Solution

Given:

An equation: $y=-x-3$ .

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 $\left(0,7\right)$ in slope-intercept form of equation as:

  $\begin{array}{l}y=mx+b\left(\text{Slope-intercept form of equation}\right)\\ y=-1\cdot x+7\left(\text{Substituting }m=-1\text{}\text{ and }b=7\right)\\ y=-x+7\end{array}$

Therefore, the equation of parallel lineto our given line is $y=-x+7$ .