Step 1
Find the equation of both lines using
[tex]\frac{y_2-y_1}{x_2-x_1}=\text{ }\frac{y-y_1}{x-x_1}[/tex]
Where,
[tex]\begin{gathered} y_1=-9 \\ y_2=\text{ -2} \\ x_1=\text{ -6} \\ x_2=1 \end{gathered}[/tex]
Hence,
[tex]\frac{-2-(-9)}{1-(-6)}=\frac{y-(-9)}{x-(-6)}[/tex][tex]\begin{gathered} \frac{7}{7}=\frac{y+9}{x+6} \\ y+9\text{ = x+6} \\ y\text{ = x+6-9} \\ y\text{ = x-}3 \end{gathered}[/tex]
For the second line we will have
[tex]\begin{gathered} \frac{-4-(-8)}{1-5}=\text{ }\frac{y-(-8)_{}}{x-5} \\ \frac{4}{-4}=\frac{y+8}{x-5} \\ -1(x-5)\text{ = y+8} \\ -x+5\text{ = y+8} \\ y\text{ =- x+5-8} \\ y\text{ = -x-3} \end{gathered}[/tex]
Step 2
Hence expressed the graphed solution as a piecewise function
[tex]f(x)=\begin{cases}x-3,-6\leq x<1 \\ \square \\ -x-3,-1
