5-6 Slope and Rates of Change

Front

What is slope?

Back

Slope is a measure of the steepness of a line, defined as the ratio of vertical change (rise) to horizontal change (run).

Front

How do you calculate slope?

Back

Slope (m) = (change in y) / (change in x) = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing an upward trend.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing a downward trend.

Front

What does a zero slope indicate?

Back

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

Front

What does an undefined slope indicate?

Back

An undefined slope occurs when a line is vertical, meaning there is no horizontal change.

Front

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

Back

The slope is 3/4.

Front

What is the slope of a line that falls 2 units for every 5 units it runs?

Back

The slope is -2/5.

Front

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

Back

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

Front

What is the formula for the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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