Chapter 8, Problem 23CCSR

To determine

To Find :The y-intercept of line m for the given points.

Answer to Problem 23CCSR

The y-intercept is 5.

Explanation of Solution

Given information:

Consider the points are $\left(–9,4\right)$ and $\left(9,6\right).$

According to line formula find the x-intercept that is

  $\left(y-y_1\right)=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)\text{where }m=\frac{y_2-y_1}{x_2-x_1}$

Here

  $\begin{array}{l}{x}_1=-9\hfill \\ x_2=9\hfill \\ y_1=4\hfill \\ y_2=6\hfill \end{array}$

Now put the points in given formula

  $\begin{array}{l}\left(y-y_1\right)=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right)\hfill \\ (y-4)=\frac{6-4}{9-(-9)}(x-(-9))\hfill \\ \begin{array}{l}(y-4)=\frac{2}{9+9}(x+9)\\ \begin{array}{l}y-4=\frac{2}{18}(x+9)\hfill \\ y-4=\frac{2}{18}\cdot x+\frac{2}{18}\cdot 9\hfill \\ \begin{array}{l}y-4=\frac{1}{9}x+1\\ y=\frac{1}{9}x+5\end{array}\hfill \end{array}\end{array}\hfill \end{array}$

Here m= $\frac{1}{9}$

Then put the value $x=0$ for find the y-intercept

  $\begin{array}{l}\begin{array}{l}y=\frac{1}{9}x+5\hfill \\ =\frac{1}{9}\left(0\right)+5\hfill \end{array} \\ =5\end{array}$

Therefore, the y-intercept is 5.