Question

Write the slope intercept from of the equation of the line that passed though the given points. ( − 1 , − 2 ) a n d ( 1 , − 4 )

Answer 1

Slope intercept form of a line passing through (-1, -2) and (1, -4) is $y= -x-3.$

Solution:

We have to find the equation of a line in slope intercept form.  

Given that  

Line is passing through point (− 1, − 2) and (1, − 4).

Equation of line passing through point $(x_1, y_1)$ and $(x_2, y_2)$ is given by,

$y-y_{1}=\frac{\left(y_{2}-y_{1}\right)}{\left(x_{2}-x_{1}\right)}\left(x-x_{1}\right) \Rightarrow(1)$

In our case $x_{1}=-1, y_{1}=-2, x_{2}=1, y_{2}=-4$

Substituting given value in (1) we get ,

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

Hence slope intercept form of a line passing through (-1, -2) and (1, -4) is $y= -x-3$