Last updated: Oct 29, 2024

Direct Variation Calculator

Q: How do you find the constant of variation?

To find the constant of direct variation k in the equation y = k ∙ x , follow these steps: Measure the value of y for an arbitrary choice of x . Divide this y by x to get k as k = y/x . Verify your result using our direct variation calculator.

Q: What is *y* in the direct variation *y = 12x*, at *x = 8*?

y = 96 . To compute this answer manually, follow these steps: Substitute x = 8 in the equation y = 12x to get y = 12 ∙ 8 . Compute the multiplication to get y = 96 . You can use our direct variation calculator for verification or further calculations.

Created by Krishna Nelaturu

Krishna Nelaturu

Krishna holds a Master's degree in Applied Mechanics and never shies away from asking questions and digging deeper. He has two years of experience in steel castings and a particular fascination for vehicle dynamics. For his thesis, Krishna developed a new optimization method to reduce squeak and rattle in premium cars. He is passionate about mathematics and physics and constantly wonders about our place in the Universe. He also loves stories and storytelling and hopes to write a book someday. See full profile

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Anna Szczepanek

PhD, Jagiellonian University in Kraków, Poland

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Holds a Ph.D. degree in mathematics obtained at Jagiellonian University. An active researcher in the field of quantum information and a lecturer with 8+ years of teaching experience. Passionate about everything connected with maths in particular and science in general. Fond of coding, she has a keen eye for detail and perfectionistic leanings. A bookworm, an avid language learner, and a sluggish hiker. She is hopelessly addicted to coffee & chocolate – the darker and bitterer, the better. See full profile

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and Adena Benn

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Adena Benn is an Information Technology teacher with a degree in Computer Science. She has been teaching high schoolers since 1996 and loves everything computers. She loves problem-solving, so creating calculators to solve real-world problems is her idea of fun. She writes children's stories, is a seamstress, and is an avid reader. In her spare time, she travels and enjoys nature. See full profile

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Table of contents

Direct variation of two variables Examples of direct variation How do you find the constant of variation?Using this direct variation calculator FAQs

Welcome to our direct variation calculator, where you can calculate the direct variation between two variables. If you're trying to determine the direct proportionality between two variables, you've come to the right place! In this article, we shall discuss the direct variation formula, real-life examples of direct variation, and how to find the constant of variation. We shall also graph the direct variation between two variables.

Direct variation of two variables

Direct proportionality or direct variation is the relationship between two variables such that an increase in one variable results in a proportional increase in the other variable. We express this relationship mathematically as:

y \propto x

Where:

$y$ - A dependant variable; and
$x$ - An independent variable.

By introducing a constant of proportionality $k$ , we obtain the direct variation formula:

y = k \cdot x

The graph of a direct variation will naturally be a straight line whose slope equals the constant $k$ .

Examples of direct variation

Before learning how to find the constant of variation $k$ , let's look at some examples of direct variation in different fields:

Ohm's law: The current $I$ flowing through a circuit directly varies with the circuit voltage $V$ . The circuit resistance $R$ is the constant of direct variation here:

\qquad V = I \cdot R

To learn more about Ohm's law, visit our Ohm's law calculator.

Newton's second law: The rate of change of the velocity of a body is directly proportional to the force applied.

\qquad \begin{align*}\mathbf{F} &\propto \frac{\text{d}\mathbf{v}}{\text{dt}}\\[1em] \mathbf{F} &= m \frac{\text{d}\mathbf{v}}{\text{dt}} = m \mathbf{a} \end{align*}

Where:

$\mathbf{F}$ - Force applied;
$\mathbf{v}$ - Velocity of the body;
$m$ -Mass of the body; and
$a$ - Acceleration of the body.

Our Newton's second law calculator will assist you in force calculations and further reading on Newton's second law.

How do you find the constant of variation?

To find the constant of direct variation k in the equation y = k ∙ x, follow these steps:

Measure the value of y for an arbitrary choice of x.
Divide this y by x to get k as k = y/x.
Verify your result using our direct variation calculator.

Using this direct variation calculator

This direct variation equation calculator is straightforward to use:

Enter the value of the independent variable x.
Provide the proportionality constant k.
- The direct variation calculator will determine the value of the dependent variable y.
- The calculator will also provide a graph of the direct variation so you can visually assess the direct proportionality.

Thanks to the versatility of this calculator, you can enter any two known parameters to find the third.

Check out how inverse proportionality works using our inverse variation calculator.

FAQs

How do you recognize direct variation?

Follow these steps to identify a direct variation between two variables x and y:

Obtain multiple measurements of the variables, x₁, y₁, x₂, y₂, x₃, y₃,..., x_n, y_n.
- If the ratio of these variables is equal, y₁/x₁ = y₂/x₂ = y₃/x₃ = ... = y_n/x_n, the variables are directly varying.
- Alternatively, plot the readings as points on a graph, (x₁, y₁), (x₂, y₂), (x₃, y₃),..., (x_n, y_n). If they form a straight line, the variables are directly varying.

What is y in the direct variation y = 12x, at x = 8?

y = 96.

To compute this answer manually, follow these steps:

Substitute x = 8 in the equation y = 12x to get y = 12 ∙ 8.
Compute the multiplication to get y = 96.
You can use our direct variation calculator for verification or further calculations.

What is the relation between the mass of objects and gravitational force?

Newton's law of universal gravitation states that the gravitational force (F) between any two objects is directly proportional to the product of their masses (m₁,m₂). Mathematically, F ∝ m₁∙m₂.

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