Slope Flashcard Review

Front

What is the definition of slope?

Back

Slope is a measure of the steepness 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 between two points (x1, y1) and (x2, y2)?

Back

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

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, meaning the line falls from left to right.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as there is no horizontal change.

Front

If a line passes through the points (2, 3) and (4, 7), what is the slope?

Back

The slope is 2, calculated as (7 - 3) / (4 - 2).

Front

What is the average rate of change?

Back

The average rate of change is the change in the value of a function divided by the change in the input value over a specific interval.

Front

How do you find the average rate of change from a table of values?

Back

Subtract the values of the function at the endpoints of the interval and divide by the difference in the input values.

Front

What is the formula for finding the rate of change of a quantity over time?

Back

Rate of change = (Final value - Initial value) / (Final time - Initial time).