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**Macleef** Find the equation of the tangent line to the curve $\displaystyle f(x) = \sqrt {x - 3}$ at the point $\displaystyle P(7,2)$.

$\displaystyle m = \lim_{x \to \-a} \frac{f(x) - f(a)}{x - a}$

$\displaystyle m = \lim_{x \to \-7} \frac{\sqrt{x - 3} - 2}{x - 7} \times \frac{\sqrt{x - 3} + 2}{\sqrt{x - 3} + 2}$

$\displaystyle m = \lim_{x \to \-7} \frac{x - 7}{(x - 7)(\sqrt {x - 3} + 2)}$

$\displaystyle m = \lim_{x \to \-7} \frac{1}{\sqrt {x - 3} + 2}$

$\displaystyle m = \frac {1}{4} $

$\displaystyle y - \frac {1}{4}x + b$

$\displaystyle 2 = (\frac {1}{4})(7) + b$

$\displaystyle \frac {-3}{4} = b$

**Therefore, **$\displaystyle y = \frac {1}{4}x + \frac {-3}{4}$

**Textbook Answer:**

$\displaystyle x - 4y + 1 = 0$

I'm confused? Don't know what I did wrong