Chapter 1.3, Problem 64E

To determine

An equation of the line passing through the pair of points $\left(\frac{7}{3},-8\right),\left(\frac{7}{3},1\right)$ and its graph.

Answer to Problem 64E

The slope − intercept form of the equation of the given line is $y=\frac{-3}{10}x-\frac{18}{10}$

Explanation of Solution

Given information :

Given pair of points $\left(\frac{7}{3},-8\right),\left(\frac{7}{3},1\right)$ .

Since slope $(m)$ of the line passing through the pair of points $(x_1,y_1),(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$

  $\begin{array}{l}for(x_1,y_1)=\left(\frac{7}{3},-8\right),(x_2,y_2)=\left(\frac{7}{3},1\right)\\ m=\frac{1+8}{\left(7/3\right)-\left(7/3\right)}\\ =\frac{9}{0}\\ \therefore m=\frac{9}{0}\end{array}$

As we know that the slope − intercept form of the equation of the line is $y-y_1=m\left(x-x_1\right)+c\mathrm{........}(1)$

Now substituting slope $m=\frac{9}{0}$ and point $(x_1,y_1)=\left(\frac{7}{3},-8\right)$ in above equation $(1)$ , we get

  $\begin{array}{l}\Rightarrow y+8=\left(\frac{9}{0}\right)\left(x-\frac{7}{3}\right)\\ \Rightarrow 0=9x-21\\ \Rightarrow 9x=21\end{array}$

  $\therefore x=\frac{7}{3}$

Hence, slope − intercept form of the equation of the given line is $x=\frac{7}{3}$

Graph: The graph of $x=\frac{7}{3}$ is

  

Interpretation: Form above graph, we can observe that the graph of line passes through the given pair of points $\left(\frac{7}{3},-8\right),\left(\frac{7}{3},1\right)$ .