# How to Write and Solve Direct Variation Equations

Direct variation equations are a fundamental concept in algebra, representing relationships where one variable changes directly in proportion to another.

Here’s a comprehensive guide on how to write and solve direct variation equations:

### 1. Understanding Direct Variation

A direct variation can be represented by the equation:

$$y = kx$$

Here, ($$y$$) and ($$x$$) are the variables that vary directly with each other, and ($$k$$) is the constant of variation or the constant of proportionality.

### 2. Writing Direct Variation Equations

To write a direct variation equation, follow these steps:

1. Identify the Variables:
Identify the two variables that are in direct variation. Let’s denote them as ($$y$$) and ($$x$$).
2. Find the Constant of Variation:
Use the given information to find the value of ($$k$$ ). This can be done by rearranging the direct variation equation as: $$k = \frac{y}{x}$$ Substitute the given values of ($$y$$) and ($$x$$) to find ($$k$$).
3. Write the Equation:
Once you have the value of ($$k$$), substitute it back into the equation ($$y= kx$$) to write the direct variation equation.

### 3. Solving Direct Variation Equations

To solve a direct variation equation, follow these steps:

1. Isolate the Variable:
If you are given a direct variation equation and asked to solve for one variable, rearrange the equation to isolate that variable. For example, to solve for ($$x$$), rearrange the equation as: $$x= \frac{y}{k}$$
2. Substitute the Given Values:
Substitute the given values of the other variable and the constant of variation into the equation and solve for the unknown variable.

### 4. Examples

#### Example 1:

Given that ($$y$$) varies directly with ($$x$$), and ($$y = 15$$) when ($$x = 5$$), write the direct variation equation and find ($$y$$) when ($$x = 10$$).

Solution:

1. Find the Constant of Variation:
$$k = \frac{y}{x} = \frac{15}{5} = 3$$
2. Write the Direct Variation Equation:
$$y = 3x$$
3. Find ($$y$$) when ($$x = 10$$):
$$y = 3 \cdot 10 = 30$$

#### Example 2:

Given the direct variation equation ($$y = 4x$$), find ($$x$$) when ($$y = 20$$).

Solution:

1. Rearrange the Equation to Solve for ($$x$$):
$$x = \frac{y}{4}$$
2. Substitute the Given Value of ($$y$$):
$$x = \frac{20}{4} = 5$$

Direct variation equations represent simple proportional relationships between two variables. By understanding the form of the equation ($$y=kx$$) and how to isolate variables, you can easily write and solve direct variation equations for various problems in mathematics and science.

## Related to This Article

### What people say about "How to Write and Solve Direct Variation Equations - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.

X
45% OFF

Limited time only!

Save Over 45%

SAVE $40 It was$89.99 now it is \$49.99