Investigating the linear equations of maximum and minimum slope lines on a linear graph in high school physics experiments using numerical method

Abstract

This study investigates the maximum and minimum slope lines of a linear graph used in high school physics experiments. The uncertainty of the graph is calculated by considering the steepest and shallowest possible lines. However, manually drawing these lines can be challenging. Thus, this research employs numerical calculation method to determine the slopes of the two straight lines that pass through the number of error bar of y-data as much as possible. These lines are drawn between the lower edge of the error bars and the upper edge of the error bars of two data points on the graph. Two case studies are conducted using physics’ experimental data, which includes three columns; x-data, averaged y-data and standard deviation of the sampling distribution of means. The results are presented as data points with error bars on graph, along with the maximum and the minimum slope lines and their corresponding linear equations. Further analysis of uncertainties of slope and Y-intercept can be performed using these equations. These findings are valuable for researchers, educators, and students to interpret and report the results. In addition, a web application is presented to facilitate the determination, further enhancing the study’s accessibility and usefulness.