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 (y = mx + b). It is calculated as the change in y (rise) over the change in x (run).

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?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as x increases, y 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 change in y regardless of the change in x.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the change in x is 0, leading to division by zero.

Front

If the slope of a line is 3, what does this mean in terms of rise and run?

Back

A slope of 3 means that for every 1 unit you move to the right (run), the line rises 3 units (rise).

Front

Find the slope between the points (1, 2) and (4, 5).

Back

The slope is (5 - 2) / (4 - 1) = 3 / 3 = 1.

Front

Find the slope between the points (2, 3) and (6, 7).

Back

The slope is (7 - 3) / (6 - 2) = 4 / 4 = 1.

Front

What is the slope of the line represented by the equation y = -2x + 4?

Back

The slope is -2.