Calculating Slope

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 (rise) to the horizontal change (run) 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 positive slope indicate about a line?

Back

A positive slope indicates that as the x-values increase, the y-values also increase, meaning the line rises from left to right.

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, meaning the line falls from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, 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 it represents a division by zero in the slope formula.

Front

How can you determine if a slope is zero from a graph?

Back

A slope is zero if the line is horizontal, meaning there is no rise over the run.

Front

What is the significance of a slope of 1?

Back

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

Front

What is the formula for finding 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.

Front

How do you interpret a slope of -5/3?

Back

A slope of -5/3 indicates that for every 3 units you move to the right (increase in x), the line moves down 5 units (decrease in y).