Slope

Front

What is the definition of slope?

Back

Slope is a measure of the steepness or incline of a line, typically represented as 'm' in the slope formula.

Front

What does a positive slope indicate about a line?

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 line?

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 formula?

Back

The slope formula is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

How do you calculate the slope from a graph?

Back

To calculate the slope from a graph, determine the 'rise' (vertical change) and 'run' (horizontal change) between two points on the line, then divide rise by run.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change regardless of the horizontal change.

Front

What is the slope of a vertical line?

Back

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

Front

How can you determine the slope from two points on a line?

Back

To determine the slope from two points, use the formula m = (y2 - y1) / (x2 - x1) with the coordinates of the two points.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change, such as speed, growth, or decline in various real-world contexts.

Front

How do you interpret a slope of 1/2?

Back

A slope of 1/2 means that for every 2 units you move horizontally to the right, the line rises 1 unit vertically.