Determining Proportional Relationships

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

How do you find the constant of proportionality?

Back

To find the constant of proportionality (k), divide one quantity by the other when they are in a proportional relationship.

Front

If 14 sticks of pepperoni are needed for 28 pizzas, how many sticks are needed for 1 pizza?

Back

To find the number of sticks needed for 1 pizza, divide 14 sticks by 28 pizzas, which equals 0.5 sticks per pizza.

Front

If a car travels 420 miles in 8 hours, what is its speed in miles per hour?

Back

Speed = Distance / Time = 420 miles / 8 hours = 52.5 miles per hour.

Front

What does it mean if a graph is proportional?

Back

A graph is proportional if it passes through the origin (0,0) and has a constant slope.

Front

If k = 3, what does this mean in a proportional relationship?

Back

It means that for every unit increase in the independent variable, the dependent variable increases by 3 units.

Front

What is the formula for a proportional relationship?

Back

The formula is y = kx, where k is the constant of proportionality.

Front

If a recipe requires 2 cups of flour for 4 servings, how much flour is needed for 10 servings?

Back

Using the constant of proportionality, 2 cups / 4 servings = 0.5 cups per serving. For 10 servings: 0.5 cups/serving * 10 servings = 5 cups.

Front

What is the relationship between ratios and proportions?

Back

Ratios compare two quantities, while proportions state that two ratios are equal.

Front

If a graph shows a straight line that does not pass through the origin, is it proportional?

Back

No, if a graph does not pass through the origin, it is not a proportional relationship.