Finding 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 'm' in the equation of a line (y = mx + b). 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 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 does a slope of zero mean?

Back

A slope of zero means the line is horizontal, indicating that there is no change in y as x changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs when a line is vertical, meaning there is no change in x as y changes, leading to division by zero in the slope formula.

Front

Find the slope of the line represented by the points (2, 3) and (5, 7).

Back

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

Front

Find the slope of the line represented by the points (1, 2) and (1, 5).

Back

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

Front

Find the slope of the line represented by the points (0, 0) and (4, 4).

Back

The slope is (4 - 0) / (4 - 0) = 4 / 4 = 1.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.