Chapter 1, Problem 20RE

To determine

To find : the equation of the line. And draw the graph of the line.

Answer to Problem 20RE

the equation of line is $y=\frac{4}{3}$.

Explanation of Solution

Given information :

Points are $\left(7,\frac{4}{3}\right),\left(9,\frac{4}{3}\right)$.

Formula used :

Slope of the line passing through the points is $\frac{y_2-y_1}{x_2-x_1}$

The equation of line is $y=mx+c$.

Calculation: since the points are $\left(7,\frac{4}{3}\right),\left(9,\frac{4}{3}\right)$ ,

So the Slope of the line passing through the points is $\frac{y_2-y_1}{x_2-x_1}$

  $\begin{array}{l}\frac{y_2-y_1}{x_2-x_1}=\frac{\frac{4}{3}-\left(\frac{4}{3}\right)}{9-\left(7\right)}\text{ [substitute]}\\ \frac{y_2-y_1}{x_2-x_1}=\frac{0}{2}\text{ [simplify]}\\ \frac{y_2-y_1}{x_2-x_1}=0\text{ [divide]}\end{array}$

Now, substitute the value of slope in the equation,

Since slope of the line is zero it means the line is parallel to x -axis, so the equation,

  $y=c$

Now find the value of $c$ , substitute $x=7,y=\frac{4}{3}$

  $\begin{array}{l}y=c\\ \frac{4}{3}=c\text{ [substitute }x=7,y=\frac{4}{3}]\\ c=\frac{4}{3}\text{ [simplify}]\end{array}$

Thus, the equation of the line is $y=\frac{4}{3}$.

By using the graphing utility the graph of line can be observed as: