 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?

## Real-World Math Made Easy

See other experiments from the lab book.

 1 Walk the Line - Straight Line Distance Graphs 2 Making Cents of Math: Linear Relationship between Weight and Quantity 3 Pool Plunge - Linear Relationship between Water Depth and Pressure 4 Funnel Volumes - Volume and Weight 5 Keep It Bottled Up - Rates of Pressure Increase 6 Graph It in Pieces: Piecewise Defined Functions 7 Mix It Up - Mixing Liquids of Different Temperatures 8 Spring Thing - Newton's Second Law 9 Stretch It to the Limit - The Linear Force Relation for a Rubber Band 10 What Goes Up - Position and Time for a Cart on a Ramp 11 That's the Way the Ball Bounces - Height and Time for a Bouncing Ball 12 Walk This Way - Definition of Rate 13 Velocity Test - Interpreting Graphs 14 From Here to There - Applications of the Distance Formula 15 Under Pressure - The Inverse Relationship between Pressure and Volume 16 Light at A Distance - Distance and Intensity 17 Chill Out: How Hot Objects Cool 18 Charging Up, Charging Down - Charging a Capacitor 19 Bounce Back - The Pattern of Rebound Heights 20 Sour Chemistry - The Exponential pH Change 21 Stepping to the Greatest Integer: The Greatest Integer Function 22 Swinging Ellipses - Plotting an Ellipse 23 Crawling Around: Parametric Plots 24 Lights Out! - Periodic Phenomena 25 Tic, Toc: Pendulum Motion 26 Stay Tuned: Sound Waveform Models 27 Up And Down: Damped Harmonic Motion 28 How Tall? Describing Data with Statistical Plots 29 And Now, the Weather - Describing Data with Statistics 30 Meet You at the Intersection: Solving a System of Linear Equations 31 Titration Curves: An Application of the Logistic Function

### Experiment 2 from Real-World Math Made Easy Lab Book #### Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.