Slope

Front

What is slope?

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 (change in y) over the run (change in x).

Front

How is slope calculated?

Back

Slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What does a positive slope indicate?

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?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing a downward trend.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no change in y as x changes.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as it would involve division by zero (change in x is 0).

Front

If a line rises 4 units for every 2 units it runs, what is the slope?

Back

The slope is 4/2 = 2.

Front

What is the slope of the line represented by the equation y = 3x + 1?

Back

The slope is 3, which is the coefficient of x.

Front

How does the slope affect the graph of a linear equation?

Back

The slope determines the angle of the line; a steeper slope means a steeper angle, while a flatter slope means a gentler angle.

Front

What is the slope of the line segment connecting points (1, 2) and (3, 6)?

Back

The slope is (6 - 2) / (3 - 1) = 4 / 2 = 2.