Proportional, Linear, Rate of Change

Front

What is a constant rate of change?

Back

A constant rate of change means that the quantity changes by the same amount over equal intervals of time. It is represented by the slope of a linear function.

Front

How do you calculate the rate of change from a graph?

Back

The rate of change can be calculated by finding the slope of the line, which is the change in the y-values divided by the change in the x-values (rise/run).

Front

What does it mean if a graph is linear?

Back

A linear graph means that the relationship between the variables can be represented by a straight line, indicating a constant rate of change.

Front

What is a proportional relationship?

Back

A proportional relationship is one where two quantities maintain a constant ratio, and the graph of the relationship passes through the origin (0,0).

Front

What is the significance of the origin in proportional relationships?

Back

In proportional relationships, the graph must pass through the origin (0,0) to indicate that when one quantity is zero, the other is also zero.

Front

What does a negative rate of change indicate?

Back

A negative rate of change indicates that as one quantity increases, the other quantity decreases.

Front

What is the formula for calculating slope?

Back

The formula for calculating slope (m) is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What does it mean if a graph is non-linear?

Back

A non-linear graph indicates that the relationship between the variables does not have a constant rate of change and cannot be represented by a straight line.

Front

How can you tell if a function is linear from its equation?

Back

A function is linear if it can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the difference between proportional and non-proportional relationships?

Back

Proportional relationships have a constant ratio and pass through the origin, while non-proportional relationships do not maintain a constant ratio and may not pass through the origin.