Chapter 2.1, Problem 41E

To determine

To find: an equation parallel to a given graph and passes through given point.

Answer to Problem 41E

  $y=2x+6$

Explanation of Solution

Given information:

  $\begin{array}{l}y=2x+5\mathrm{...}\text{(1)}\\ \left(x_1,y_1\right)=\left(0,6\right)\mathrm{...}\text{(2)}\end{array}$

Calculation:

Compare equation (1) with slope intercept equation to get,

  $m=5$

Slopes of parallel lines are equal. So, line parallel to $y=2x+5$ will have slope $\left(m\right)=2$ .

Substitute the given point and value of slope in the slope equation and solve as follows:

  $\begin{array}{c}y-y_1=m\left(x-x_1\right)\\ y-6=\left(2\right)\left(x-0\right)\\ y-6=2x\\ y=2x+6\end{array}$

An equation parallel to a $y=2x+5$ and passes through $\left(0,6\right)$ is $y=2x+6$ .