Finding Slope

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

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 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 horizontal change (run) is 0, leading to division by zero.

Front

Find the slope of the line passing through the points (2, 3) and (5, 7).

Back

The slope is (7 - 3) / (5 - 2) = 4 / 3.

Front

Find the slope of the line passing through the points (1, 2) and (1, 5).

Back

The slope is undefined because the x-coordinates are the same (1), indicating a vertical line.

Front

If a line has a slope of 2, what does this mean in terms of rise and run?

Back

For every 2 units of rise, there is a 1 unit run, meaning the line rises steeply.

Front

What is the slope of the line represented by the equation y = -3x + 4?

Back

The slope is -3, indicating the line falls steeply as x increases.