Question

True or false? Give an explanation for your answer. For any two points in the plane, there is a linear function whose graph passes through them.

Name: Problem 79, Chapter 1: Calculus Single Variable
Uploaded: 2021-05-04T13:05:32-08:00
Duration: 1 min 24 s
Channel: Gregory Higby
Description: True or false? Give an explanation for your answer. For any two points in the plane, there is a linear function whose graph passes through them.

   True or false? Give an explanation for your answer.
For any two points in the plane, there is a linear function whose graph passes through them.

Calculus Single Variable

Deborah… 7th Edition

Chapter 1, Problem 79

Instant Answer

Solved by Expert Gregory Higby

05/04/2021

Step 1

A linear function is a function that can be graphically represented in the plane by a line. This means that for any two distinct points in the plane, there is a unique line that passes through them. Show more…

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True or false? Give an explanation for your answer. For any two points in the plane, there is a linear function whose graph passes through them.

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Key Concepts

Linear Function

A linear function is an expression of the form f(x) = mx + b, where m represents the slope and b represents the y-intercept. This type of function graphs to a straight line in the coordinate plane and is a fundamental concept in algebra and calculus, representing constant rates of change.

Uniqueness of a Line through Two Points

In Euclidean geometry, any two distinct points determine exactly one line. This principle guarantees that for any pair of distinct points in the plane, there exists a unique linear function (or equation of a line) whose graph passes through both points.

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