SLOPE

Front

What is the definition of slope?

Back

The slope of a line is a measure of its steepness, usually represented by the letter 'm'. It is 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, indicating no vertical change as the x-value changes.

Front

What is the slope of a vertical line?

Back

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

Front

Given the points (2, 3) and (5, 11), calculate the slope.

Back

m = (11 - 3) / (5 - 2) = 8 / 3.

Front

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

Back

The slope (m) is 4, which indicates the line rises 4 units for every 1 unit it moves to the right.

Front

If a line has a slope of -3/4, what does this tell you about its direction?

Back

The line falls from left to right, decreasing in value as x increases.

Front

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

Back

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