Question

Find the equation of the line parallel to the line $y=2x+1$and containing the point $(3,5)$. Express your answer in slope–intercept form and graph the line.

Short answer

The equation of the line is$y=2x-1$

The graph can be given as

Step-by-step solution

Given information

We are given a equation of the line as$y=2x+1$

Find the slope of the parallel line

The equation of the given line is $y=2x+1$.

Comparing with standard equation the slope of the line is $2$.The slope of the parallel line is $2$.

Hence the equation becomes$y=2x+b$

Find the y-intercept

To find the y-intercept substitute the given coordinates in the equation

We have,

$$\begin{gathered} y=2x+b \\ 5=2\left(3\right)+b \\ b=5-6 \\ b=-1 \end{gathered}$$

Hence the equation becomes

$y=2x-1$

Plot the graph of lines

The graph can be given as

Conclusion

The equation of the line is$y=2x-1$

The graph can be given as