SLOPE from All Representations

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 do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The 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-value increases, the y-value also increases, 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-value increases, the y-value decreases, 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-value changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as there is no horizontal change.

Front

How can slope be represented in a linear equation?

Back

In a linear equation of the form y = mx + b, 'm' represents the slope of the line.

Front

What is the rate of change in a real-world context?

Back

The rate of change refers to how one quantity changes in relation to another, often represented as slope in a graph.

Front

How do you interpret the slope in a real-world scenario, such as a price increase?

Back

The slope indicates how much the price increases (rise) for each unit of time or quantity sold (run).

Front

What is the significance of the slope in a graph of a linear relationship?

Back

The slope indicates the strength and direction of the relationship between the two variables represented on the graph.