Understanding Point and Slope in Linear Equations and Approximations: A Case Study

Authors

Kyunghee Moon

Volume

21

Issue

3

Abstract

This article delves into an intervention designed to enhance a precalculus student’s understanding in constructing linear equations and in approximating function values. Before the intervention, the student primarily relied on the algebraic formula y₂-y₁/x₂-x₁ to determine slope, knew slope geometrically as Δ_y/Δ_x solely for integer values, and struggled to construct a linear equation without an explicitly shown y-intercept. Through the intervention, the student comprehended slope m as a unit rate and expanded this understanding to Δy = 𝑚Δ𝑥 for integer Δx by iterating m, Δ𝑥 number of times. She also successfully used this newfound understanding to construct linear equations, including tangent line equations, and approximate function values. Nonetheless, she faced some challenges in comprehending Δy = 𝑚Δ𝑥 for non-integer Δ𝑥 and in conceiving point as a multiplicative object with its coordinates representing covarying quantities. Further exploration is needed to validate these findings and address potential difficulties that students might face in grasping slope in the context of linear equations and approximations.

First Page

541

Last Page

568

Recommended Citation

Moon, Kyunghee (2024) "Understanding Point and Slope in Linear Equations and Approximations: A Case Study," The Mathematics Enthusiast: Vol. 21 : No. 3 , Article 3.
DOI: https://doi.org/10.54870/1551-3440.1642
Available at: https://scholarworks.umt.edu/tme/vol21/iss3/3

Digital Object Identifier (DOI)

10.54870/1551-3440.1642

Publisher

University of Montana, Maureen and Mike Mansfield Library