Chapter 13.3, Problem 9PSB

To determine

To find: The point-slope form, an equation of the line containing a given point and the point of intersection of the given two graphs.

Answer to Problem 9PSB

The point-slope form is $y=5x-9$ .

Explanation of Solution

Given:

The given point that line contains is:

  $\left(2,1\right)$

The given equations are:

  $\begin{array}{l}x+2y=15\left(1\right)\\ 3x-y=3\left(2\right)\end{array}$

Calculation:

The point(s) of intersection of equation $\left(1\right)\&\left(2\right)$ is calculated as:

  $\begin{array}{c}x+6x+2y-2y=15+6\left[\text{multiply equation}\left(2\right)\text{ by 2\& add to equation}\left(1\right)\right]\\ 7x=21\\ x=3\\ 3\left(3\right)-y=3\left[\text{put }x=3\text{ in equation }\left(2\right)\right]\end{array}$

Further simplified as:

  $y=6$

Therefore the point(s) of intersection $\left(1\right)\&\left(2\right)$ is $\left(3,6\right)$ .

The point-slope form of required line that passes through the given point and the point of intersection of the given two graphs is as:

  $\begin{array}{c}y-1=\frac{6-1}{3-2}\left(x-2\right)\\ y-1=5\left(x-2\right)\\ y=5x-9\end{array}$

Therefore the point-slope form is $y=5x-9$ .