Chapter 9.4, Problem 66S

To determine

To find: Write an equation of the line passing through each pair of points.

Answer to Problem 66S

The equation for the circle is $y-1=0$ .

Explanation of Solution

Given information:

The given pair of points is,

  $\left(7,1\right)\text{and}\left(7,8\right)$

The slope-intercept form is

  $y=mx+b\mathrm{...}\left(1\right)$

Where $m$ is the slope and $b$ is the $y$ -intercept

The given points are $\left(x_1=7,y_1=1\right)$ and $\left(x_2=7,y_2=8\right)$

To find the slope we calculated as,

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{8-1}{7-7}\\ m=0\end{array}$

Substitute the value of $m$ in equation $\mathrm{...}\left(1\right)$

  $\begin{array}{c}y=mx+b\\ 1=0\times 7+b\\ 1=0+b\\ b=1\end{array}$

Substitute the values of $m=0,b=1$ in equation $\mathrm{...}\left(1\right)$

  $\begin{array}{l}y=0\times x+1\\ y=1\\ y-1=0\end{array}$

Thus, the equation of the line passing through the points is $y-1=0$ .