Question

-1x - 5 intersects the line f(x) = 3x + 11

Answer 1

(-4, -1)

Explanation

When one line intersects the other one, the next condition is satisfied:

`k(x)=f(x)`

Substituting with the equations of each line and solving for x:

`\begin{gathered} -x-5=3x+11 \\ -x-5+x-11=3x+11+x-11 \\ -16=4x \\ (-16)/(4)=(4x)/(4) \\ -4=x \end{gathered}`

Substituting x = -4 into the formula of f(x), we get:

`\begin{gathered} f(x)=3x+11 \\ f(-4)=3(-4)+11 \\ f(-4)=-12+11 \\ f(-4)=-1 \end{gathered}`

Finally, the intersection point is:

`\begin{gathered} (x,f(x)) \\ (-4,-1) \end{gathered}`