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Show that the slope of a line is independent of the points on the line used to compute it.

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 9

Elements of Geometry

Derivatives

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University of Michigan - Ann Arbor

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Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

01:35

Find an equation of the li…

00:54

Verify that the points $(0…

01:17

Explain how to find the eq…

01:44

Describe how to find the s…

We're going to verify that the 0.0 B and one comma A plus B. Lie on the line. Y equals X plus B. Let's start with the zero comma. B zero is my X. Value and B is my Y. Value. So we're going to plug those in. We get B equals eight is A times X. Which is zero plus B. I get B equals a times zero is zero plus B, B equals B. That's a true statement. So this is a true true point. On that line. Over here we have Y equals A X plus B, Y, S. A plus B equals eight times 1 Plus B. A plus B. Eight times one is A plus B, A plus B equals A plus B. That is a true statement. So this point also lies on the line. Therefore A. Is the slope.

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