Lesson 4.1-Rate of Change and Proportional Relationships

Front

What is the unit rate?

Back

The unit rate is a comparison of any two units of measure in which the second term is 1. It shows how much of one quantity corresponds to one unit of another quantity.

Front

How do you find the unit rate from a given total cost and quantity?

Back

To find the unit rate, divide the total cost by the quantity. For example, if apples cost $3.60 for 3 pounds, the unit rate is $3.60 ÷ 3 = $1.20 per pound.

Front

What does a point (x, y) represent in a proportional relationship?

Back

In a proportional relationship, the point (x, y) represents the quantity y that corresponds to x units of another quantity.

Front

How do you calculate the average rate of change between two points?

Back

The average rate of change is calculated by taking the difference in the y-values and dividing it by the difference in the x-values. Formula: (y2 - y1) / (x2 - x1).

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other quantity is constant.

Front

If a car travels 120 miles in 2 hours, what is the unit rate of speed?

Back

The unit rate of speed is 60 miles per hour, calculated as 120 miles ÷ 2 hours.

Front

What does the term 'rate of change' refer to?

Back

Rate of change refers to how much one quantity changes in relation to another quantity. It is often expressed as a ratio.

Front

Find the unit rate of 624 calories in 3 servings.

Back

The unit rate is 208 calories per serving, calculated as 624 calories ÷ 3 servings.

Front

What is the significance of the unit rate in real-life situations?

Back

The unit rate helps compare prices, speeds, and other quantities, making it easier to make informed decisions.

Front

How can you represent a proportional relationship on a graph?

Back

A proportional relationship can be represented by a straight line that passes through the origin (0,0) on a graph.