Dependent and Independent Variables
Aligned to 6.EE.C.9 — Common Core State Standards for Mathematics.
What this lesson teaches
The independent variable is the one you change freely; the dependent variable is the result that responds to it. An equation connects them, and you can show the same relationship in a table or a graph.
Worked examples
Example 1
A bus travels 40 miles each hour: d = 40t. Time t is independent, distance d depends on it. At t = 3, d = 40 × 3 = 120 miles.
Example 2
A plant grows 2 cm per week: h = 2w. Week is independent, height depends on it. At w = 6, h = 12 cm.
Example 3
On a graph, the independent variable goes on the x-axis and the dependent one on the y-axis. Put time on x and you can read the story left to right.
Practice questions
- In y = 5x, which variable is independent and which is dependent?
- A phone plan costs $2 per gigabyte: write an equation and find the cost for 6 GB.
- Make a table of y = 3x for x = 0, 1, 2, and 3.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
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Variables Dependientes e Independientes
La variable independiente es la que cambias libremente; la variable dependiente es el resultado que responde a ella. Una ecuación las conecta, y puedes mostrar la misma relación en una tabla o una gráfica.
Ejemplo 1: Un autobús recorre 40 millas cada hora: d = 40t. El tiempo t es independiente, la distancia d depende de él. En t = 3, d = 40 × 3 = 120 millas.
Ejemplo 2: Una planta crece 2 cm por semana: h = 2s. La semana es independiente, la altura depende de ella. En s = 6, h = 12 cm.
Ejemplo 3: En una gráfica, la variable independiente va en el eje x y la dependiente en el eje y. Pon el tiempo en x y puedes leer la historia de izquierda a derecha.
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