Equation of the Tangent Line

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$Equation of a Tangent Line Example 1$

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Equation of the Tangent Line Worksheet 1

Equation of the Tangent Line Worksheet 2

Equation of the Tangent Line Worksheet 3

Equation of the Tangent Line Worksheet 5

Equation of the Tangent Line Worksheet 6

Remember that a tangent line of a graph at a point is a line that just barely touches the graph at that particular point. It skims against the edge of the graph, as opposed to cutting through it (which is what the secant line does).

In order to find the equation of the tangent line to a curve, perform the following steps:

Take the derivative of the original function
Plug the point where the original function and the tangent line meet into the derivative. The number you get as the solution is the slope of the tangent line
Plug the slope found in Step 2, and the point of intersection between the original function and the tangent line, into the point-slope formula for the equation of the line, which is shown below, where $(x_1,y_1)$ is the point of intersection, and $m$ is the slope you found in Step 2.

$y-y_1=m(x-x_1)$

Simplify the equation of the tangent line as much as possible. This is your final answer.

Equation of the Tangent Line

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