Introduction to Graphing and Structure

Overview

This lecture is to explain the introduction to graph paper, methods of making graphs on it, types of graphs, and related scientific concepts.

Structure of Graph Paper

• Graph paper has large boxes, small boxes, and the smallest boxes.
• One large box contains four small boxes, and each small box contains five smallest boxes.
• While making graphs, 70-80% of the graph paper area should be used.
• The scale on the x-axis (usually independent variable) and y-axis (dependent variable) is increased at equal intervals.
• Always write the unit and scale on each axis; clarify how many boxes correspond to what value.

Making and Reading Graphs

• The independent variable (e.g., time) is taken on the x-axis and the dependent variable (e.g., distance) on the y-axis.
• The value difference of each box should be equal, for example, each smallest box value is 0.4 seconds.
• Patterns in graphs can be straight lines (direct relation), curves, horizontal lines, vertical lines, etc.
• Learn to read relations and patterns from graphs, such as a straight line indicating a direct proportional relationship.

Variables: Independent and Dependent

• Independent variable — the value you change, usually on the x-axis.
• Dependent variable — the value that changes with the independent variable, usually on the y-axis.
• Example: When time changes, distance changes; so time is independent and distance is dependent.

Types of Graphs and Trends

• Different graphs show different relationships: direct, inverse, constant.
• Boyle’s Law shows an inverse relation between pressure and volume.
• In an isochoric process, volume remains constant, and the graph forms a vertical line.
• In an isobaric process, pressure remains constant, and the graph forms a horizontal line.

Best Fit Line and Error Bars

• Best fit line — the straight line passing closest to the data points.
• Error bar — represents uncertainty or measurement error in data; smaller error bar = less uncertainty.

Extrapolation and Absolute Zero

• Extrapolation — predicting values beyond the data range of the graph.
• Absolute Zero (-273.15°C or 0 Kelvin) — the temperature at which gas molecules stop moving.
• Extrapolation is used to estimate such temperatures where actual measurement is not possible.

Key Terms & Definitions

• Graph Paper — lined paper with square boxes.
• Independent Variable — taken on the x-axis, whose value is decided by oneself.
• Dependent Variable — taken on the y-axis, which changes according to input.
• Best Fit Line — the straight line closest to the graph's data points.
• Error Bar — a line showing uncertainty.
• Extrapolation — estimating values beyond the data.
• Absolute Zero — the lowest possible temperature, -273.15°C.

Action Items / Next Steps

• Keep graph paper, pencil, scale ready, and practice making x-y graphs yourself by correctly writing scale, labels, and units.
• Next topic: reading significant figures.