Chapter 9.4, Problem 65S

To determine

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

Answer to Problem 65S

The equation for the circle is ${(x-3)}^2+{\left(y-\left(-2\right)\right)}^2=37$ .

Explanation of Solution

Given information:

The given pair of points is,

  $\left(-2,5\right)\text{and}\left(3,1\right)$

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 $\left(x_1=-2,y_1=5\right)$ and $\left(x_2=3,y_2=1\right)$

To find the slope we calculated as,

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{1-5}{3-\left(-2\right)}\\ m=\frac{-4}{5}\end{array}$

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

  $\begin{array}{c}y=mx+b\\ 5=\frac{-4}{5}\times -2+b\\ 5=\frac{8}{5}+b\\ b=\frac{17}{5}\end{array}$

Substitute the values of $m=\frac{-4}{5},b=\frac{17}{5}$ in equation $\mathrm{...}\left(1\right)$

  $\begin{array}{l}y=\frac{-4}{5}x+\frac{17}{5}\\ 5y=-4x+17\\ 4x+5y=17\end{array}$

Thus, the equation of the line passing through the points is $4x+5y=17$ .