Slope and Rate of Change

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented as the ratio of the vertical change to the horizontal change between two points on the line.

Front

How is slope calculated using two points (x1, y1) and (x2, y2)?

Back

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

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal.

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical.

Front

What is the slope of a line that descends from left to right?

Back

The slope of a line that descends from left to right is negative.

Front

What is the slope of a line that ascends from left to right?

Back

The slope of a line that ascends from left to right is positive.

Front

If a line has a slope of -1, what does this imply about its angle?

Back

A slope of -1 implies that the line descends at a 45-degree angle.

Front

What is the slope of a line represented by the equation y = -5/3x + 2?

Back

The slope of the line is -5/3.

Front

How can you determine if a slope is positive, negative, or undefined from a graph?

Back

A positive slope rises from left to right, a negative slope falls from left to right, and an undefined slope is represented by a vertical line.

Front

What is the relationship between slope and rate of change?

Back

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