We need the equation for the line going through the points (-3, 1) and (-1, -1).
To do this we write the equation of the line as:
[tex]y=mx+b[/tex]The slope m can be calculated as the ratio of the difference of the y-coordinates and the difference of the x-coordinates:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{(-1)-1}{(-1)-(-3)}=\frac{-2}{2}=-1[/tex]Knowing the slope, we can calculate the y-intercept b using one of the points and replacing in the equation:
[tex]\begin{gathered} y=(-1)x+b \\ -1=(-1)(-1)+b \\ -1=1+b \\ b=-1-1=-2 \end{gathered}[/tex]The equation of the line is: y=-x-2
