Question

Find the equation of the straight line passing through the points$(-1,1)$ and$(2,-4)$.

Answer 1

Step 1: Compute the slope:

Given points :$(-1,1)$ and $(2,-4)$

Let, $(x_1,y_1)=(-1,1)$ and $(x_2,y_2)=(2,-4)$

$\therefore$Slope $m=\frac{(y_2–y_1)}{(x_2–x_1)}$

$$\begin{gathered} m=\frac{(-4–1)}{(2+1)} \\ m=\frac{-5}{3} \end{gathered}$$

Step 2: Compute the equation:

We know that the equation of a line passing through points $(x_1,y_1)$and $(x_2,y_2)$is, $(y–y_1)=m(x–x_1)$ where$m$ is the slope of the line.

By substituting the value in the formula we get,

$$\begin{gathered} \Rightarrow (y–1)=\frac{-5}{3}(x+1) \\ \Rightarrow 3y-3=-5x-5 \\ \Rightarrow 5x+3y+2=0 \end{gathered}$$

Hence, the equation of the straight line passing through the points$(-1,1)$ and$(2,-4)$ is $5x+3y+2=0$.