What is the name of the line whose slope is equal to the average change of a function?

Answer 1

A secant line connects two points on a curve.

The slope of the secant line is calculated using the formula: (y₂ – y₁) / (x₂ – x₁)

The equation of the line through the two points can be found by using the slope-point formula:

y – y₁ = m(x – x₁)

Answer 2

Hi, Peter,

I'm actually unsure if I'm giving you the correct information, but please check the Khan Academy lesson at: https://www.khanacademy.org/math/calculus-all-old/taking-derivatives-calc/using-the-formal-definition-of-derivative-calc/a/tangent-lines-and-rates-of-change

Is the line you are thinking of called the tangent? It is the line that measures the slope of a function at a point. between two points on that function.

Bob