Grades Sixth Grade Expressions & EquationsDependent and Independent Variables

Dependent and Independent Variables

📐 Expressions & Equations

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Dependent and Independent Variables

One variable drives the other — figure out which is which.

In a relationship between two quantities, the independent variable is the one you choose or control (the input). The dependent variable changes based on the independent variable (the output). We plot independent variables on the x-axis and dependent variables on the y-axis.

Independent Variable

The input / causeYou choose its valueGoes on the x-axisExample: number of hours worked

Dependent Variable

The output / effectIts value depends on the independent variableGoes on the y-axisExample: total pay earned

Ask: "Which variable depends on the other?" That variable is the dependent one.

🌱Writing the Equation

A plant grows 3 cm per week. Let w = weeks (independent) and h = height in cm (dependent).
Equation: h = 3w
When w = 5, h = 15 cm. When w = 10, h = 30 cm.

h = 3w \quad (\text{dependent} = \text{rate} \times \text{independent})

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Remember This!

Fill in a table of values (input/output table) to identify the pattern. If each output = the same number × input, the relationship is proportional.

✏️ Try It!

A taxi charges $2.50 per mile. If m = miles driven, which equation shows total cost C?

Take Quiz 📝 — 25 Questions