7.4A Constant Rate of Change

Front

What is a constant rate of change?

Back

A constant rate of change refers to a situation where the change in one quantity is consistent with the change in another quantity over time, often represented as a linear relationship.

Front

How do you write an equation for a constant rate of change?

Back

An equation for a constant rate of change can be written in the form y = mx + b, where m represents the rate of change and b is the y-intercept.

Front

What does the slope of a line represent in a graph of a linear relationship?

Back

The slope of a line represents the constant rate of change between the two variables plotted on the graph.

Front

If a person types 25 words per minute, how can this be expressed mathematically?

Back

This can be expressed as the equation y = 25x, where y is the total number of words and x is the time in minutes.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is zero, indicating the starting point of the relationship on the graph.

Front

How can you determine the constant rate of change from a table of values?

Back

To determine the constant rate of change from a table, calculate the difference in the y-values divided by the difference in the x-values for any two points.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The formula for calculating the slope (m) is m = (y2 - y1) / (x2 - x1).

Front

What does a negative constant rate of change indicate?

Back

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

Front

In the equation y = 3x, what does the number 3 represent?

Back

In the equation y = 3x, the number 3 represents the constant rate of change, meaning for every 1 unit increase in x, y increases by 3 units.

Front

How can you interpret a graph with a constant rate of change?

Back

A graph with a constant rate of change will show a straight line, where the slope of the line indicates the rate of change.