Slope

Front

What is the definition of slope?

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 ratio of the rise (change in y) over the run (change in x).

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 an undefined slope mean?

Back

An undefined slope occurs when a line is vertical, meaning the x-values are the same for two points, resulting in division by zero in the slope formula.

Front

What does a slope of zero indicate?

Back

A slope of zero indicates a horizontal line, meaning there is no change in y as x changes.

Front

Find the slope of the line through the points (1, 2) and (3, 6).

Back

The slope is 2, calculated as (6 - 2) / (3 - 1).

Front

Find the slope of the line through the points (4, 5) and (4, 9).

Back

The slope is undefined, as the x-values are the same (4).

Front

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

Back

The slope is 0, as the y-values are the same (3).

Front

What is the slope of a line that rises 3 units for every 4 units it runs?

Back

The slope is 3/4.