6th Grade Independent and Dependent Variables Lesson (Free PDF)

6th Grade math lesson: Independent and Dependent Variables – Maths PDF

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This variable relationships lesson for 6th Grade covers independent and dependent variables (Common Core 6.EE.C.9), with a free PDF to print.

In an equation with two variables, the independent variable is the one you choose, and the dependent variable depends on it. For y = 3x, each y is 3 times x, and its graph is a line through the origin. For y = x + 2, each y is 2 more than x.

Grade 6 · Common Core State Standards: 6.EE.C.9

Key facts in this variable relationships lesson

Key facts

The independent variable is the input; the dependent variable is the output.
In y = kx, y is k times x and the graph passes through the origin.
In y = x + c, y is c more than x and the graph crosses the y-axis at c.
A table, a graph, and an equation can show the same relationship.
Use substitution to find y from x, and solve an equation to find x from y.

What are independent and dependent variables?

In a relationship between two quantities, the independent variable is the one you choose or change. The dependent variable is the one whose value depends on it. If a taxi charges $3 per mile, the number of miles x is independent, and the cost y is dependent.

Equation with two variables

An equation such as $y = 3x$ or $y = x + 2$ shows how the dependent variable $y$ is found from the independent variable $x$. Each x gives exactly one y.

How do you connect a table, a graph, and an equation?

Choose values of x, use the equation to find y, and record the pairs in a table. Then plot the pairs as points. For $y = 3x$, y is always 3 times x.

The value of y depends on the value of x.

The graph of y = 3x is a line through the origin.

An equation, a table, and a graph describe the same relationship.

What is different about y = x + 2?

In $y = x + 2$, you add 2 to x. The table has y values 2 more than x, and the graph is a line that crosses the y-axis at 2, not at the origin.

The graph of y = x + 2 starts at (0, 2).

Name the independent variable and the dependent variable.
Look for a pattern: does y multiply x, or add to x?
Write the equation and test it with two table values.
Use the equation to find y for any x, or x for any y.

Example: A car travels at 55 miles per hour, so $d = 55t$. To find the time for 275 miles, solve $275 = 55t$ to get $t = 5$ hours. When the unknown is the dependent variable, substitute and compute. When the unknown is the independent variable, solve an equation.

Variable relationships lesson: questions and answers

What is an independent variable?

The independent variable is the input that you choose or change, usually x. In a taxi fare problem it is the number of miles.

What is a dependent variable?

The dependent variable is the output whose value depends on the independent variable, usually y. The cost of a taxi ride depends on the miles.

How do you write an equation from a table?

Look for the pattern between each x and y. If y is always k times x, write y = kx; if y is always c more than x, write y = x + c.

Why does the graph of y = 3x go through the origin?

When x is 0, y = 3 times 0 = 0, so the point (0, 0) is on the graph.

How do you find x when you know y?

Substitute y into the equation and solve. For y = 5x and y = 40, solve 40 = 5x to get x = 8.

How to use this variable relationships lesson

Read the definitions first, then follow the worked method line by line and redo the example on paper without looking. When every step makes sense, move on to the worksheet, then check yourself with the quiz.

Download the variable relationships lesson as a PDF with the button below and keep it with your notes.

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