# Find the Tangent Line

Definition:  We know how to find the slope of the tangent line. By taking the derivative at a point, x, we can quite easily find an equation for a line tangent to a curve $f(x)$ at a point $x = a$.  We will use the point-slope formula for a line, which you may recall from algebra. The equation for a line with slope m through a point $(x_1, y_1)$ is:

Example:  Find the equation of a line tangent to the curve $f(x) = x^2 + 7x - 2$ at the point $(1, 6)$.

Solution:  First, we find the slope of the tangent line by taking the derivative at $x = 1: f'(x) = 2x + 7; f'(1) = 9$. Then, we use the point-slope equation to create a line equation:

$y - 6 = 9(x - 1)$

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