Types of Slope Flashcard

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

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, resulting in an upward trend.

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, resulting in a downward trend.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is zero, indicating no vertical change as the x-values change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as there is no horizontal change and the line goes straight up and down.

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 the line represented by the equation y = 3x + 2?

Back

The slope of the line is 3, which indicates a positive slope.

Front

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

Back

The slope of the line is -2, which indicates a negative slope.

Front

What does a slope of zero mean in a real-world context?

Back

A slope of zero means there is no change in the dependent variable as the independent variable changes, such as a flat road.

Front

What does an undefined slope mean in a real-world context?

Back

An undefined slope means there is no horizontal change, such as a vertical cliff.