Vernier Software & Technology

# Making Cents of Math: Linear Relationship between Weight and Quantity

## Introduction

The slope of a line describes its steepness. The numerical value of the slope can represent a number of other important mathematical concepts. Given any two points on a line, (x1, y1) and (x2, y2), the slope of that line can be computed using the formula:

$m = \frac{{{y_2} - {y_1}}} {{{x_2} - {x_1}}}$

where m represents the slope of the line, x1 and x2 represent the independent variable coordinates, and y1 and y2 represent the dependent variable coordinates.

In this activity you will use a Force Sensor to collect a linear set of data points. Specifically, you will measure the weight of 8, 16, 24… pennies. You will then analyze this data and interpret the meaning of the slope as it relates to the independent and dependent variables. A model will help you predict future measurements and interpret past results.

## Objectives

• Collect weight versus number data for a collection of identical pennies.
• Model the weight versus number data using a linear equation.
• Interpret the slope and intercept values from the linear model.

## Sensors and Equipment

This experiment features the following Vernier sensors and equipment.

You may also need an interface and software for data collection. What do I need for data collection?