3.2 Proportion

• Direct proportion is a relationship where two variables increase or decrease together at the same rate
• What is the relationship between miles and kilometers in direct proportion?

  1 mile = 1.6 km
• What is direct proportion?

  Same rate increase or decrease
• The formula for direct proportion is $y =$$kx$, where \( k \) is the constant of proportionality.


  True
• If one egg makes one cake, then doubling the eggs doubles the number of cakes
• What is the formula for inverse proportion?

  $y =$$\frac{k}{x}$
• Steps to differentiate direct and inverse proportion

  1️⃣ Understand the definitions of direct and inverse proportion

  2️⃣ Identify how variables change in the scenario

  3️⃣ Determine if changes are at the same rate or in opposite directions

  4️⃣ Apply the correct formula to express the relationship
• In direct proportion, if one variable is multiplied by a factor, the other variable is multiplied by the same factor.

  True
• What is the formula for inverse proportion?

  $y =$$\frac{k}{x}$
• In the formula for direct proportion, k represents the constant of proportionality.
• Match the scenario with the type of relationship:

  Miles and Kilometers ↔️ Direct Proportion

  Time and Speed ↔️ Inverse Proportion
• What is the formula for inverse proportion?

  $y =$$\frac{k}{x}$
• In inverse proportion, the product of the two variables remains constant.


  True
• In the example of miles and kilometers, if you double the miles, the kilometers double as well.
• Steps to set up and solve direct proportion problems:

  1️⃣ Identify the two directly proportional variables

  2️⃣ Write the direct proportion equation: $y =$$kx$

  3️⃣ Substitute known values into the equation

  4️⃣ Solve for the constant of proportionality, $k$

  5️⃣ Use $k$ to find the unknown value
• In the example of miles and kilometers, 1 mile equals 1.6 kilometers.
• What is the relationship between two variables in direct proportion?

  They increase together
• What happens to the number of cakes if the number of eggs increases in direct proportion?

  It increases proportionally
• 1 mile equals 1.6 kilometers in a direct proportion relationship.


  True
• Direct and inverse proportions involve variables that change in opposite directions.

  False
• In direct proportion, variables change in the same direction.


  True
• What type of relationship involves variables that move in opposite directions?

  Inverse proportion
• The constant of proportionality in direct proportion is always a positive value.

  True
• In the direct proportion equation $y =$$kx$, the term k represents the constant of proportionality.
• What does one egg make in the given example of direct proportion?

  One cake
• To solve a direct proportion, you first identify the two variables that are directly proportional.
• In inverse proportion, variables change in the same direction.

  False
• Match the inversely proportional variables with their corresponding values:

  Time ↔️ Speed

  Volume ↔️ Pressure
• What is the first step in setting up and solving an inverse proportion?

  Identify variables
• What are direct and inverse proportions used for in real-life scenarios?

  Solving problems
• To solve a problem involving inverse proportion, you first determine the value of the constant k.
• In inverse proportion, when one variable doubles, the other halves.

  True
• What does $k$ represent in the inverse proportion formula?


  Constant of proportionality
• In inverse proportion, when $x$ doubles, $y$ halves
• What key phrase indicates direct proportion?

  "Increase or decrease together"
• How do variables change in inverse proportion compared to direct proportion?

  In opposite directions
• The constant of proportionality in the example of eggs and muffins is 2.
• In inverse proportion, as one variable doubles, the other halves.

  True
• If 2 miles equals 3.2 kilometers, how many kilometers are in 5 miles?

  8 kilometers
• When solving direct proportion problems, you can use the equation $y =$$kx$.


  True