Slope

Front

What is slope?

Back

Slope is a measure of the steepness or incline of a line, typically represented as a fraction that describes the ratio of the vertical change to the horizontal change between two points on the line.

Front

How is slope represented mathematically?

Back

Slope is represented as a fraction, often written as m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, resulting in an upward trend from left to right.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, resulting in a downward trend from left to right.

Front

What does a zero slope indicate?

Back

A zero slope indicates that the line is horizontal, meaning there is no vertical change as the x-value changes.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates that the line is vertical, meaning there is no horizontal change as the x-value changes.

Front

Calculate the slope between the points (2, 3) and (6, 7).

Back

The slope is (7 - 3) / (6 - 2) = 4 / 4 = 1.

Front

Calculate the slope between the points (1, 2) and (1, 5).

Back

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

Front

If a line has a slope of 4, what does this mean?

Back

This means that for every 1 unit increase in the x-direction, the y-value increases by 4 units.

Front

If a line has a slope of -1/4, what does this mean?

Back

This means that for every 4 units increase in the x-direction, the y-value decreases by 1 unit.