## Definition of a tangent line with slope m

### A tangent line is a straight line that touches a curve at a specific point in such a way that it has the same slope as the curve at that point

A tangent line is a straight line that touches a curve at a specific point in such a way that it has the same slope as the curve at that point.

More formally, if we have a curve represented by a function y = f(x), and we want to find the tangent line to the curve at a specific point (x₁, y₁), then the tangent line will have the same slope as the curve at that point.

The slope of a line is given by the formula m = (change in y) / (change in x) = (y₂ – y₁) / (x₂ – x₁), where (x₂, y₂) is any other point on the line.

So, if the slope of the tangent line at a particular point is known and denoted as m, the equation of the tangent line can be written as y – y₁ = m(x – x₁).

In summary, a tangent line has the same slope as the curve it touches at a specific point, and the equation of the tangent line can be found using the point-slope form, given the slope and coordinates of the point of tangency.

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