Chapter 4, Problem 7CT

To determine

To calculate: To write the equation of line in point-slope form

Answer to Problem 7CT

Equation of line in point slope form is $y-2=-\frac{1}{3}\left(x+3\right)$

Explanation of Solution

Given: Line passing through $\left(-3,2\right)$ and $\left(6,-1\right)$

Formula Used:

Equation of line passing through two points is given as

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

Calculation:

Given that the line passes through $\left(-3,2\right)$ and $\left(6,-1\right)$

Thus, equation of line is calculated as follows:

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

Substituting the values:

  $\begin{array}{l}y-2=\frac{-1-2}{6-\left(-3\right)}\left(x-\left(-3\right)\right)\\ y-2=\frac{-3}{6+9}\left(x+3\right)\\ y-2=\frac{-3}{9}\left(x+3\right)\\ y-2=-\frac{1}{3}\left(x+3\right)\end{array}$

Conclusion:

Hence, equation of line is $y-2=-\frac{1}{3}\left(x+3\right)$