Question

How do you write an equation of a line that passes through points $(-1,3),(2,-3)$?

Answer 1

Finding the equation of the line:

Consider the given points $(-1,3)$ and $(2,-3)$.

As the equation of the line passing through the point $(x_1,y_1)$ and $(x_2,y_2)$ is given by $y-y_1=m(x-x_1)$:

Here, $m$ is the slope given by the formula:

$m=\frac{(y_2-y_1)}{(x_2-x_1)}$

Step -1. Find the slope:

Substituting the given points $(-1,3)$ and $(2,-3)$ in the equation of a line:

$\begin{array}{rcl}m& =& \frac{(-3-3)}{(2-(-1\left)\right)}\\ & \Rightarrow & m=\frac{-6}{3}\\ & \Rightarrow & m=-2\end{array}$

Step- 2. Find the equation of the line:

Substituting the value of $m$ as $-2$ and $(x_1,y_1)$ as $(-1,3)$ in the equation of the line $y-y_1=m(x-x_1)$:

$\begin{array}{rcl}y-3& =& -2(x+1)\\ & \Rightarrow & y-3=-2x-2\\ & \Rightarrow & y=-2x+1\\ & \Rightarrow & 2x+y=1\end{array}$

Hence, the equation of a line passing through the point $(-1,3)$ and $(2,-3)$ is $2x+y=1$.