Graphic Relationships & Rate of Change Vocabulary

Vocabulary flashcards covering graphic relationships, rate of change, slope, scatter plots, temporal and spatial scales, and scientific notation based on the lecture transcript.

Variable

Something that can change or be measured.

Relationship Between Variables

When one variable changes, the other changes in a predictable way.

Direct Relationship

A relationship where as $X$ increases, $Y$ increases, causing both variables to move in the same direction.

Inverse Relationship

A relationship where as $X$ increases, $Y$ decreases, causing the variables to move in opposite directions.

Cyclic Relationship

A relationship where $Y$ increases and decreases in a predictable, repetitive pattern or wave.

Constant Relationship

A relationship where as $X$ increases, $Y$ stays the same, appearing as a horizontal line on a graph.

Slope

The steepness of a line on a graph.

Rate

How much something changes over a certain amount of something else, usually time.

Constant Rate

A rate of change where the variable changes at a steady rate, represented visually by a straight line.

Increasing Rate

A rate of change where the variable is changing faster and faster, causing the graph line to get steeper.

Decreasing Rate

A rate of change where the variable is changing slower and slower, causing the graph line to get flatter.

Scatter Plot

A graph that uses individual points to show the relationship between two variables.

Line of Best Fit

A line drawn through a scatter plot that shows the overall trend or general relationship between two variables.

Change

A difference in a variable over time.

Stability

When something stays the same or remains relatively unchanged.

Cyclic Change

A change that repeats in a predictable pattern, such as day and night.

Non-cyclic Change

A change that does not repeat in a predictable cycle, such as a volcanic eruption.

Temporal Scale

The amount of time over which a change occurs.

Short Temporal Scale

A change that happens over a relatively short period of time, such as weather changing during a single day.

Long Temporal Scale

A change that happens over a long period of time, such as the formation of mountains.

Spatial Scale

The size of the area over which a change occurs.

Local Scale

A spatial scale describing a change affecting a small area, such as a thunderstorm in one town.

Regional Scale

A spatial scale describing a change affecting a larger region, such as a hurricane affecting several states.

Global Scale

A spatial scale describing a change affecting Earth as a whole, such as global climate change.

Basic Rate Formula

$$\text{Rate} = \text{change} \div \text{time}$$

Compound Unit

A unit made from two or more units, such as $\text{km/h}$.

Speed Formula

$$\text{Speed} = \text{distance} \div \text{time}$$

Scientific Notation

A method used for writing very large or very small numbers easily in the basic form $a \times 10^n$, where $a$ is between 1 and 10.

One Thousand (Power of 10)

$10^3$, which contains 3 zeros.

Ten Thousand (Power of 10)

$10^4$, which contains 4 zeros.

One Million (Power of 10)

$10^6$, which contains 6 zeros.

One Billion (Power of 10)

$10^9$, which contains 9 zeros.

One Trillion (Power of 10)

$10^{12}$, which contains 12 zeros.