Rates, Unit Rates, and Slope

Front

What is a slope in mathematics?

Back

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

Front

How is slope calculated between two points (x1, y1) and (x2, y2)?

Back

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 an undefined slope?

Back

An undefined slope occurs in vertical lines where the change in x is zero, making the slope calculation (y2 - y1) / (x2 - x1) impossible.

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities where one of the quantities is expressed as a single unit, often used to express cost per item.

Front

If 5 pounds of apples cost $10, how do you find the unit rate?

Back

To find the unit rate, divide the total cost by the total weight: $10 / 5 pounds = $2 per pound.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change in various contexts, such as speed, cost per item, or growth rates.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, indicating no vertical change as the x-value changes.

Front

What is the slope of a vertical line?

Back

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