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 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 y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation of the line y = mx + b.

Front

How can you find the x-intercept of a line?

Back

The x-intercept is found by setting y = 0 in the equation of the line and solving for x.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

The slope can represent rates of change in various contexts, such as speed, growth, or decline, making it essential for interpreting data.

Front

How does the slope relate to the concept of rate in real-world scenarios?

Back

The slope represents the rate of change, such as speed (distance over time) or rainfall (amount over time), indicating how one quantity changes in relation to another.

Front

What is the relationship between slope and parallel lines?

Back

Parallel lines have the same slope, meaning they rise and run at the same rate and will never intersect.