Do two points always determine a linear function?

In a geometric context, two distinct points ??1 and ??2 always determine a unique line in the Cartesian plane (this is one of the basic postulates of Euclidean geometry). Only the non-vertical lines, however, can be described by the graph of a function ??(??)=????+??. This task focuses on producing an explicit function ??(??) as long as the line is not vertical.

This problem allows the student to think geometrically about lines and then relate this geometry to linear functions. Or the student can work algebraically with equations to find the explicit equation of the line through two points (when that line is not vertical).
Resource ID#: 43512 Type: Problem-Solving Task
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General Information

Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators educators, Students , Parents
Suggested Technology: Adobe Acrobat Reader, Microsoft Office
Instructional Time: 15 Minute(s)
Keywords: Do two points always determine an exponential function?, exponential function, linear function, cpalms, icpalms, illustrativemathematics.org, illustrative mathematics, tasks, mathematics, math, resource, free, freely available, problems-based learning, student activities, Florida Standards
Instructional Component Type(s): Problem-Solving Task
Resource Collection: Illustrative Mathematics

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