Comparing Rate of Change

Front

What is the rate of change?

Back

The rate of change is a measure of how much a quantity changes in relation to another quantity. It is often represented as the slope of a line in a graph.

Front

How do you calculate the rate of change between two points (x1, y1) and (x2, y2)?

Back

Rate of change = (y2 - y1) / (x2 - x1). This formula calculates the slope of the line connecting the two points.

Front

What does a positive rate of change indicate?

Back

A positive rate of change indicates that as one quantity increases, the other quantity also increases.

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 slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the ratio of the vertical change to the horizontal change between two points on the line.

Front

If a line has a slope of 0, what does that mean?

Back

A slope of 0 means that the line is horizontal, indicating that there is no change in the y-value as the x-value changes.

Front

If a line has an undefined slope, what does that mean?

Back

An undefined slope occurs when a line is vertical, indicating that the x-value does not change as the y-value changes.

Front

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

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

How can you determine if two lines have the same rate of change?

Back

Two lines have the same rate of change if they have the same slope.

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph.