Proportional Relationships Study Guide

What is the unit rate if 4 apples cost $2?

• 0.25 dollars per apple

• 0.5 dollars per apple

• 1 dollar per apple

• 2 dollars per apple

Answer explanation

To find the unit rate, divide the total cost by the number of apples. Here, $2 ÷ 4 apples = $0.5 per apple. Thus, the correct answer is 0.5 dollars per apple.

Fill in the blank: The constant ratio or unit rate can be found by dividing one quantity by the other, for example, if y is the dependent variable and x is the independent variable, then k = ____.

• A) x/y

• B) y/x

• C) x+y

• D) y-x

Answer explanation

The constant ratio k is defined as the dependent variable y divided by the independent variable x. Therefore, k = y/x, making option B the correct choice.

What does the slope of the line represent in a graph of a proportional relationship?

• The constant of proportionality

• The variable rate

• The dependent variable

• The independent variable

Answer explanation

In a graph of a proportional relationship, the slope represents the constant of proportionality, indicating how much the dependent variable changes for a unit change in the independent variable.

What is the general form of a proportional relationship?

• y = kx

• y = x + k

• y = k - x

• y = x/k

Answer explanation

The general form of a proportional relationship is represented by the equation y = kx, where k is a constant. This indicates that y varies directly with x, making it the correct choice.

What is 25% as a fraction?

• 1/4

• 1/5

• 1/2

• 1/3

Answer explanation

25% means 25 out of 100, which simplifies to 1/4. Therefore, 25% as a fraction is 1/4, making it the correct choice.

In a proportional relationship, the point (0, 0) represents the situation where both quantities are ____.

• zero

• one

• equal

• different

Answer explanation

In a proportional relationship, the point (0, 0) indicates that both quantities are zero. This is because at this point, neither quantity has any value, confirming that they are both at the same level of zero.

Set up the ratio: 3/4 = x/10. What is the value of x?

• 7.5

• 6

• 8

• 7

Answer explanation

To find x, cross-multiply: 3 * 10 = 4 * x. This gives 30 = 4x. Dividing both sides by 4, we get x = 30/4 = 7.5. Thus, the correct answer is 7.5.

A car travels 60 miles in 1 hour. How far will it travel in 3.5 hours?

• 180 miles

• 210 miles

• 200 miles

• 220 miles

Answer explanation

The car travels at a speed of 60 miles per hour. In 3.5 hours, it will travel 60 miles/hour * 3.5 hours = 210 miles. Therefore, the correct answer is 210 miles.

Which of the following is a tip for success in understanding proportionality?

• Ignore ratios

• Use real-world examples

• Avoid graphs

• Memorize formulas

Answer explanation

Using real-world examples helps to visualize and relate to proportionality concepts, making them easier to understand. This approach enhances comprehension compared to ignoring ratios, avoiding graphs, or just memorizing formulas.

Fill in the blank: Always check that your ___ are consistent when determining proportionality.

• graphs

• ratios

• examples

• formulas

Answer explanation

The correct choice is 'ratios' because proportionality is determined by comparing ratios. Ensuring that your ratios are consistent is essential for establishing proportional relationships.