7-5-6 Slope and Rates of Change

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

What does a positive slope indicate about a graph?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, showing a direct relationship.

Front

What does a negative slope indicate about a graph?

Back

A negative slope indicates that as the x-values increase, the y-values decrease, showing an inverse relationship.

Front

What is a constant rate of change?

Back

A constant rate of change means that the change in the dependent variable is consistent for equal changes in the independent variable, represented by a straight line on a graph.

Front

What is a variable rate of change?

Back

A variable rate of change means that the change in the dependent variable is not consistent for equal changes in the independent variable, represented by a curved line on a graph.

Front

Can a graph with an undefined slope have a constant rate of change?

Back

Yes, a graph with an undefined slope (like a vertical line) can represent a constant rate of change in certain contexts, such as time.

Front

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

Back

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

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no change in the y-value as the x-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the change in x is 0, leading to division by zero.

Front

If a line has a slope of 1, what does this mean?

Back

A slope of 1 means that for every unit increase in x, there is a corresponding unit increase in y, indicating a 45-degree angle.