Chapter 5.3, Problem 41E

To determine

To calculate:

The equation of the line passing through the point $\left(0,6\right)$ which is parallel to $y=5x-3$

Answer to Problem 41E

The equation of the line passing through the point $\left(0,6\right)$ which is parallel to $y=5x-3$ is

  $5x-y=-6$ .

Explanation of Solution

Given information:

  $\begin{array}{l}\left(0,6\right)\\ y=5x-3\end{array}$

Formula used:

The equation of the line passing through the point $\left(x_1,y_1\right)$ and parallel to $y=mx+c$ is given by the following expression:

  $y-y_1=m\left(x-x_1\right)$

Calculation:

The point is considered as $\left(x_1,y_1\right)=\left(0,6\right)$

The given equation of line $y=5x-3$ is compared with $y=mx+c$ , get that:

  $m=5,c=-3$

The equation of the line passing through the point $\left(x_1,y_1\right)=\left(0,6\right)$ and parallel to $y=5x-3$ is given by the following expression:

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ y-6=5\left(x-0\right)\\ y-6=5x\\ 5x-y=-6\end{array}$