Slope: Rise over Run

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 'm' in the equation of a line. It is calculated as the ratio of the rise (vertical change) to the run (horizontal change).

Front

How is slope calculated using two points on a line?

Back

The slope (m) can be calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

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, as there is no vertical change (rise) regardless of the horizontal change (run).

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the run is 0 and division by zero is not possible.

Front

If a line has a slope of 1, what does this imply about the rise and run?

Back

A slope of 1 implies that for every unit of rise, there is an equal unit of run, meaning the line rises at a 45-degree angle.

Front

How can you determine the slope from the equation of a line in slope-intercept form?

Back

In the slope-intercept form of a line, y = mx + b, the slope (m) is the coefficient of x.

Front

What is the slope of the line represented by the equation y = -2x + 3?

Back

The slope of the line is -2, as it is the coefficient of x in the equation.

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.