Slope intercept form of a line passing through (-1, -2) and (1, -4) is [tex]y= -x-3.[/tex]
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 [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by,
[tex]y-y_{1}=\frac{\left(y_{2}-y_{1}\right)}{\left(x_{2}-x_{1}\right)}\left(x-x_{1}\right) \Rightarrow(1)[/tex]
In our case [tex]x_{1}=-1, y_{1}=-2, x_{2}=1, y_{2}=-4[/tex]
Substituting given value in (1) we get ,
[tex]\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}[/tex]
Hence slope intercept form of a line passing through (-1, -2) and (1, -4) is [tex]y= -x-3[/tex]
