Chapter 4, Problem 5CR

To determine

The equation of the line in the slope-intercept form that is parallel to the line $y=2x+1$ and containing the point $\left(3,5\right)$ and graph the line.

Answer to Problem 5CR

Solution:

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

  

Explanation of Solution

Given information:

The line is parallel to the line $y=2x+1$ and passing through the point $\left(3,5\right)$

An equation of a line with slope $m$ and $y\text{-}$ intercepts $b$ is $y=mx+b$

Here, the given equation of the line is $y=2x+1$

Compare the above equation line with the line $y=mx+b$

  $\Rightarrow m=2,b=1$ .

Hence, the slope of the line is $m=2$

Two non-vertical lines are parallel, if and only if their slopes are equals and they have different $y\text{-}$ intercepts.

Thus, the equation of the line parallel to the line $y=2x+1$ has the slope $m=2$

The equation of the line passing through the point $\left(x_1,y_1\right)$ with slope $m$ is given as $y-y_1=m\left(x-x_1\right)$

Here, the slope is $m=2$ and the point is $\left(3,5\right)$

Compare the given point $\left(3,5\right)$ with $\left(x_1,y_1\right)$ , then $x_1=3,y_1=5$

The equation becomes

  $y-5=2\left(x-3\right)$

  $\Rightarrow y=2x-6+5$

  $\Rightarrow y=2x-1$

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

To draw the graph of the function, plot the given point $\left(3,5\right)$

As slope is $2=\frac{2}{1}=\frac{rise}{run}$ , move $1$ unit to the right and $2$ unit above.

This gives the point $\left(4,7\right)$ lies on the line.

Draw the line through these two points.