Rate of Change of Linear Functions Warmup 2

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the slope, which represents the ratio of the change in the y-value to the change in the x-value.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates that the line is vertical, meaning it does not have a defined rate of change.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no change in the y-value as the x-value changes.

Front

If a line has a slope of -1, what does this tell you about the rate of change?

Back

A slope of -1 indicates that for every unit increase in x, the y-value decreases by 1 unit.

Front

What is the significance of a positive slope in a linear function?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship.

Front

What is the significance of a negative slope in a linear function?

Back

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

Front

How can you determine if a function is linear based on its rate of change?

Back

A function is linear if its rate of change (slope) is constant across all intervals.

Front

What is the formula for calculating the rate of change in a real-world context?

Back

Rate of change = (Change in quantity) / (Change in time).

Front

If a car travels 100 miles in 2 hours, what is the rate of change in miles per hour?

Back

Rate of change = 100 miles / 2 hours = 50 miles per hour.