Chapter E, Problem 13.7EX

To determine

To find the equation of line passing through $(-3,5)$ and $(2,8)$ .

Answer to Problem 13.7EX

Option (b)

Explanation of Solution

Given information: Points $(-3,5)$ and $(2,8)$ .

Concept used:

The equation of line passing through $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is

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

The equation of line passing through $(-3,5)$ and $(2,8)$ is

  $\begin{array}{l}y-5=\left(\frac{8-5}{2+3}\right)(x+3)\\ y-5=\frac{3}{5}(x+3)\\ 5y-25=3x+9\\ 3x-5y+34=0\end{array}$

The equation of the line is $3x-5y=-34$

  $\begin{array}{l}y-7=-\frac{3}{2}(x+4)\\ y=-\frac{3}{2}x+1\end{array}$

Hence, the equation of line is $y=-\frac{3}{2}x+1$