Chapter 4, Problem 11PT

To determine

To Write: An equation of line in slope intercept form that passes through point $\left(2,-3\right)$ and is parallel to line $y=4x-9$

Answer to Problem 11PT

An equation of line is $y=4x-11$

Explanation of Solution

Given information:

Line passes through point $\left(2,-3\right)$ and is parallel to line $y=4x-9$

Concept and Formula Used:

Slope intercept form $y=mx+c$ where $m$ is slope and $c$ is intercept.

Point slope form of a line: $y-y_1=m\left(x-x_1\right)$

Parallel lines: If lines are parallel then the slopes of lines are equal

Calculation:

The required line is parallel to

  $y=4x-9$

Now, find the slope of given line by comparing it with $y=mx+c$ .

The slope of line $y=4x-9$ is $4$ .

Let the slope of required line be ‘m’. As the required line is parallel to $y=4x-9$

Therefore, the slope of required line is equal to slope of $y=4x-9$ i.e. $m=4$

The required line passes through $\left(2,-3\right)$ and having slope $4$ . Using point slope form of equation of line

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ \text{where }\left(x_1,y_1\right)=\left(2,-3\right)\&m=4\\ y-\left(-3\right)=4\left(x-2\right)\\ y+3=4x-8\left(\text{Distributive property}\right)\\ \text{Subtract 3 from both sides}\\ y+3-3=4x-8-3\\ y=4x-11\end{array}$

Conclusion:

An equation of line is $y=4x-11$