Slope

Front

What is the definition of slope in mathematics?

Back

Slope is a measure of the steepness or incline of a line, typically represented 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) can be 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-coordinate increases, the y-coordinate 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-coordinate increases, the y-coordinate 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 regardless of the horizontal change.

Front

What is the slope of a vertical line?

Back

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

Front

How can you determine which of two lines is steeper?

Back

The steepness of a line can be determined by comparing the absolute values of their slopes; the line with the greater absolute value of slope is steeper.

Front

If a line has a slope of -2, what does this tell you about its direction?

Back

A slope of -2 indicates that for every 1 unit increase in the x-direction, the line decreases by 2 units in the y-direction, meaning it falls steeply from left to right.

Front

What is the slope of the line passing through the points (3, 7) and (-1, 9)?

Back

The slope is calculated as m = (9 - 7) / (-1 - 3) = 2 / -4 = -1/2.

Front

What is the slope of the line passing through the points (12, 16) and (8, 12)?

Back

The slope is calculated as m = (12 - 16) / (8 - 12) = -4 / -4 = 1.