Chapter 1, Problem 22RE

To determine

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

Answer to Problem 22RE

the equation of line is $y=-\frac{4}{3}x+\frac{22}{3}$.

Explanation of Solution

Given information :

Points are $\left(1,6\right),\left(4,2\right)$.

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 $\left(1,6\right),\left(4,2\right)$ ,

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

  $\begin{array}{l}\frac{y_2-y_1}{x_2-x_1}=\frac{2-\left(6\right)}{4-\left(1\right)}\text{ [substitute]}\\ \frac{y_2-y_1}{x_2-x_1}=\frac{-4}{3}\text{ [simplify]}\\ \frac{y_2-y_1}{x_2-x_1}=-\frac{4}{3}\text{ [divide]}\end{array}$

Now, substitute the value of slope in the equation,

Since slope of the line $m=-\frac{4}{3}$ , so the equation,

  $\begin{array}{l}y=mx+c\\ y=-\frac{4}{3}x+c\text{ [substitute]}\end{array}$

Now find the value of $c$ , substitute $x=1,y=6$

  $\begin{array}{l}y=-\frac{4}{3}x+c\\ 6=-\frac{4}{3}\left(1\right)+c\text{ [substitute }x=1,y=6]\\ c=\frac{22}{3}\text{ [simplify}]\end{array}$

Thus, the equation of the line is $y=-\frac{4}{3}x+\frac{22}{3}$.

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