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 to the horizontal change between two points on the line.

Front

How is slope calculated from 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, 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 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 because the change in x is 0, leading to division by zero.

Front

How can you determine the slope from a table of values?

Back

To determine the slope from a table, calculate the change in y (rise) and the change in x (run) between two points, then use the slope formula.

Front

What does an undefined slope represent in terms of line orientation?

Back

An undefined slope represents a vertical line, where the x-coordinates are the same for all points on the 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).

Front

What are some methods to find the slope of a line?

Back

Methods to find the slope include using two points on the line, calculating from a table of values, or using the slope-intercept form of a linear equation.