The equation of the line is [tex]y=\frac{-1}{5} x-\frac{21}{5}[/tex].
Solution:
The points on the line are (–6, –3) and (4, –5).
[tex]x_{1}=-6, y_{1}=-3, x_{2}=4, y_{2}=-5[/tex]
Slope of the line:
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]$m=\frac{-5-(-3)}{4-(-6)}[/tex]
[tex]$m=\frac{-5+3}{4+6}[/tex]
[tex]$m=\frac{-2}{10}[/tex]
[tex]$m=\frac{-1}{5}[/tex]
Point-slope formula:
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
[tex]$y-(-3)=\frac{-1}{5}(x-(-6))[/tex]
[tex]$y+3=\frac{-1}{5}(x+6)[/tex]
[tex]$y+3=\frac{-1}{5} x-\frac{6}{5}[/tex]
Subtract 3 from both sides of the equation.
[tex]$y=\frac{-1}{5} x-\frac{21}{5}[/tex]
The equation of the line is [tex]y=\frac{-1}{5} x-\frac{21}{5}[/tex].
