Answer
(-4, -1)
Step-by-step explanation
When one line intersects the other one, the next condition is satisfied:
[tex]k(x)=f(x)[/tex]
Substituting with the equations of each line and solving for x:
[tex]\begin{gathered} -x-5=3x+11 \\ -x-5+x-11=3x+11+x-11 \\ -16=4x \\ \frac{-16}{4}=\frac{4x}{4} \\ -4=x \end{gathered}[/tex]
Substituting x = -4 into the formula of f(x), we get:
[tex]\begin{gathered} f(x)=3x+11 \\ f(-4)=3(-4)+11 \\ f(-4)=-12+11 \\ f(-4)=-1 \end{gathered}[/tex]
Finally, the intersection point is:
[tex]\begin{gathered} (x,f(x)) \\ (-4,-1) \end{gathered}[/tex]
