# Chapter 2 - Section 2.7 - Derivatives and Rates of Change - 2.7 Exercises: 20

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 $$(l): y=4x-23$$

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