Chapter 8.6, Problem 48E

To determine

What is an equation of the line that is parallel to the line $y=5x+3$ and passes through $\left(0,-1\right)$ .

Answer to Problem 48E

The equation of parallel lineto our given line is $y=5x-1$ and option F is the correct choice.

Explanation of Solution

Given:

Four choices: $\text{F}\text{. }y=5x-1\text{ G}\text{. }y=-5x-1\text{ H}\text{. }y=\frac{1}{5}x-1\text{ I}\text{. }y=-\frac{1}{5}x-1$ .

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 $5$ . So, the slope of parallel line to our given line will be $5$ .

Now we will substitute the slope and y -intercept $\left(0,-1\right)$ in slope-intercept form of equation as:

  $\begin{array}{l}y=mx+b\left(\text{Slope-intercept form of equation}\right)\\ y=5x+(-1)\left(\text{Substituting }m=5\text{ and }b=-1\right)\\ y=5x-1\end{array}$

Therefore, the equation of parallel lineto our given line is $y=5x-1$ and option F is the correct choice.