3.1 Rate of Change

Front

What is the definition of 'slope' in mathematics?

Back

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

Front

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

Back

Slope (m) = (y2 - y1) / (x2 - x1)

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line falls from left to right.

Front

What is the average rate of change?

Back

The average rate of change is the change in the value of a function divided by the change in the input value over a specified interval.

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, indicating a constant rate of change.

Front

What is the formula for finding the average rate of change between two points?

Back

Average Rate of Change = (f(b) - f(a)) / (b - a) where a and b are the input values.

Front

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

Back

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

Front

What is the significance of a slope of 1?

Back

A slope of 1 indicates that for every unit increase in x, there is an equal unit increase in y, resulting in a 45-degree angle line.

Front

How can you determine if a table represents a linear relationship?

Back

A table represents a linear relationship if the differences between consecutive y-values divided by the differences in x-values are constant.