Rate of Change and Slope

Front

What is the definition of slope?

Back

Slope is a measure of the steepness or incline of a line, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between 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 on the graph.

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 on the graph.

Front

What does a zero slope indicate?

Back

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

Front

What does an undefined slope indicate?

Back

An undefined slope occurs when a line is vertical, meaning there is no horizontal change as the y-value changes.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

Find the slope of the line that passes through the points (2, 3) and (4, 7).

Back

Slope = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

If a line has a slope of -3, what does this tell you about the line?

Back

The line decreases steeply as it moves from left to right.