Proportional Relationships (Equations) Worksheet

Free printable and online worksheets to help Grade 7 students review how to identify the constant of proportionality in a proportional relationship as and recognize it as the unit rate in the context of a given situation. Find and interpret the constant of proportionality within the contexts of problems. Relate the equations to a corresponding ratio table or graphical representation.

Proportional Relationships In Equations

A proportional relationship between two variables 𝑥 and 𝑦 is one where the ratio of 𝑦 to 𝑥 is constant. This relationship can be described by a simple linear equation of the form 𝑦 = 𝑘𝑥, where 𝑘 is the constant of proportionality.

Characteristics of Proportional Relationships in Equations

1. Direct Variation: The equation 𝑦 = 𝑘𝑥 shows that 𝑦 varies directly with 𝑥.
2. Constant Ratio: The ratio 𝑦/𝑥 = 𝑘 is constant for all values of 𝑥 and 𝑦.
3. Graph: The graph of a proportional relationship is a straight line that passes through the origin (0, 0).

Solving Problems with Proportional Relationships
To solve problems involving proportional relationships, follow these steps:

1. Identify the Constant of Proportionality: Determine the constant 𝑘 from the given information.
2. Write the Equation: Use the form 𝑦 = 𝑘𝑥 to write the equation representing the relationship.
3. Solve for the Unknown: Use the equation to find the unknown value by substituting the known values.

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