Chapter 13, Problem 2CT

To determine

Write an equation of MN, if $\text{M (-2, 1)}$ and $\text{N (2, 4)}$ .

Answer to Problem 2CT

The equation of MN $3x-4y=-10$

Explanation of Solution

Given information :

  $\text{M (-2, 1)}$ and $\text{N (2, 4)}$ .

The slope of the line MN = $\frac{y-y_1}{x-x_1}$

  $\begin{array}{l}\frac{y-y_1}{x-x_1}=m\\ (x_1,y_1)=(-2,1)\\ \frac{y-1}{x-(-2)}=\frac{4-1}{2-(-2)}\\ \frac{y-1}{x+2}=\frac{3}{4}\\ 4(y-1)=3(x+2)\\ 4y-4=3x+6\\ 3x-4y=-10\end{array}$

Hence,

The equation of MN $3x-4y=-10$