Answer
The equation of the tangent line $l$ is $$(l): y=4x-23$$
Work Step by Step
According to definition, the slope of the tangent line $l$ to the graph of $y=g(x)$ at $x=5$ is the derivative of $g(x)$ at $x=5$, or in other words, $g'(5)$.
Therefore, we can write the formula of the tangent line $l$ is $$(l): y=g'(5)x+b$$$$(l):y=4x+b$$
We also notice that at $x=5$, $y=g(5)=-3$.
So, applying the formula of the tangent line $l$, we have $$4\times5+b=-3$$$$20+b=-3$$$$b=-23$$
Therefore, the equation of the tangent line $l$ is $$(l): y=4x-23$$
