Comparing Slopes

Front

What is the definition of slope in mathematics?

Back

The slope is a measure of the steepness or incline of a line, calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise over run).

Front

How do you determine if one slope is greater than another?

Back

Compare the numerical values of the slopes; the larger the value, the steeper the line.

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, showing an upward trend.

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, showing a downward trend.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The formula is m = (y2 - y1) / (x2 - x1).

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 y = mx + b.

Front

If two lines have the same slope, what can be said about their relationship?

Back

If two lines have the same slope, they are parallel and will never intersect.

Front

What does it mean if a slope is zero?

Back

A slope of zero means the line is horizontal, indicating that there is no change in the y-value as the x-value changes.

Front

What is the significance of a slope of undefined?

Back

An undefined slope occurs in vertical lines, where the x-value does not change, indicating a vertical relationship.

Front

How can you visually compare slopes on a graph?

Back

You can visually compare slopes by looking at the angles of the lines; steeper lines have greater slopes.