Chapter 8.6, Problem 18E

To determine

To find:

The equation of the line that is parallel to the given line and passes through $\left(0,4\right)$ .

Answer to Problem 18E

The equation of parallel lineto our given line is $y=2x+4$ .

Explanation of Solution

Given:

An equation: $y=2x+1$ .

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 $2$ .So, the slope of parallel line to our given line will be $2$ .

Now we will substitute the slope and y -intercept $\left(0,4\right)$ in slope-intercept form of equation as:

  $\begin{array}{l}y=mx+b\left(\text{Slope-intercept form of equation}\right)\\ y=2x+4\left(\text{Substituting given values}\right)\end{array}$

Therefore, the equation of parallel lineto our given line is $y=2x+4$ .