Rate of Change

Front

What is the formula to calculate the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

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

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

Front

What is the average rate of change of a function over an interval?

Back

The average rate of change is the change in the function's value divided by the change in the input value over that interval.

Front

How do you interpret a positive slope?

Back

A positive slope indicates that as the independent variable increases, the dependent variable also increases.

Front

How do you interpret a negative slope?

Back

A negative slope indicates that as the independent variable increases, the dependent variable decreases.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

If the slope of a line is 2, what does this mean in terms of rate of change?

Back

It means that for every 1 unit increase in x, the value of y increases by 2 units.

Front

What is the relationship between the slope of a line and the concept of 'rise over run'?

Back

The slope is defined as 'rise over run', which is the vertical change (rise) divided by the horizontal change (run) between two points on the line.

Front

How do you find the slope from a linear equation in the form y = mx + b?

Back

In the equation y = mx + b, m represents the slope of the line.