Slope & Rate of Change

Front

What is the definition of slope?

Back

The slope is a measure of the steepness or incline of a line, calculated as the ratio of the vertical change to the horizontal change between two points on the line.

Front

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

Back

Slope (m) = (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 a direct relationship.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

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

What does the slope represent in a real-world context?

Back

The slope represents the rate of change in a situation, such as speed or growth rate.

Front

If a sloth runs 6 feet in 1 minute, what is the slope of the line representing its speed?

Back

The slope is 6 feet per minute.

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is constant and is represented by the slope.

Front

How can you determine if a slope is constant from a table of values?

Back

If the differences in y-values divided by the differences in x-values are the same for all pairs of points, the slope is constant.