Geometry A 2.2 Slope of a Line

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm'. It is calculated as the change in y (rise) divided by 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 about a line?

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 about a line?

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 vertical line?

Back

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

Front

What is the slope of a horizontal line?

Back

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

Front

If the slope of a line is 1, what does this mean?

Back

A slope of 1 means that for every unit increase in x, y increases by the same amount, resulting in a 45-degree angle.

Front

What is the slope of the line between the points (2, 3) and (4, 7)?

Back

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

Front

What is the slope of the line between the points (1, 2) and (1, 5)?

Back

The slope is undefined because the x-coordinates are the same, indicating a vertical line.

Front

What is the slope of the line between the points (0, 0) and (3, 3)?

Back

The slope is (3 - 0) / (3 - 0) = 3 / 3 = 1.