Rate of Change and Slope

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.8.EE.B.5

Front

What does a slope of zero mean?

Back

A slope of zero means that there is no vertical change as the x-value changes, indicating a horizontal line.

Tags

CCSS.8.EE.B.5

Front

What does an undefined slope mean?

Back

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

Tags

CCSS.8.EE.B.5

Front

How do you calculate the average rate of change?

Back

The average rate of change is calculated by taking the difference in the y-values divided by the difference in the x-values between two points.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

If a climber is at 400 feet after 2 hours and 700 feet after 6 hours, what is the average rate of change?

Back

The average rate of change is 75 feet per hour.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the formula for slope using two points (x1, y1) and (x2, y2)?

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

Given the points (1, 2) and (3, 6), what is the slope?

Back

The slope is 2.

Tags

CCSS.8.EE.B.5

Front

What is the slope of a line represented by the equation y = 3x + 2?

Back

The slope of the line is 3.

Tags

CCSS.8.EE.B.5