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The given equation is:

\[
\frac{2}{7} \left( x - \frac{2}{5} \right) = y + \frac{1}{3}
\]

Let's convert this to the standard form, which generally means having everything on one side of the equation, typically in the form \( Ax + By + C = 0 \).

### Step 1: Expand the left side
Distribute the \(\frac{2}{7}\) over the terms inside the parentheses:

\[
\frac{2}{7} \left( x - \frac{2}{5} \right) = \frac{2}{7}x - \frac{2}{7} \cdot \frac{2}{5}
\]

\[
\frac{2}{7}x - \frac{4}{35} = y + \frac{1}{3}
\]

### Step 2: Eliminate the fractions
To eliminate fractions, find the least common denominator (LCD) for all terms. The denominators are 7, 35, and 3. The LCD is 105.

Multiply the entire equation by 105:

\[
105 \left( \frac{2}{7}x - \frac{4}{35} \right) = 105 \left( y + \frac{1}{3} \right)
\]

This simplifies to:

\[
15(2x) - 3(4) = 105y + 35
\]

\[
30x - 12 = 105y + 35
\]

### Step 3: Move all terms to one side
Move all terms to one side to get a standard form equation:

\[
30x - 105y - 12 - 35 = 0
\]

\[
30x - 105y - 47 = 0
\]

Thus, the equation in standard form is:

\[
30x - 105y - 47 = 0
\]

Would you like more details on any part of this solution?

### Related Questions:
1. How can you convert a different linear equation to standard form?
2. What is the geometric interpretation of the standard form of a line?
3. How can you eliminate fractions from an equation with different denominators?
4. How does converting to standard form help in graphing the equation?
5. How can you check if your equation in standard form is equivalent to the original equation?

### Tip:
When converting to standard form, always try to eliminate fractions first by multiplying through by the least common denominator (LCD).

Convert this to standard form: (2/7)(x - 2/5) = y + 1/3

Learn how to convert the equation (2/7)(x - 2/5) = y + 1/3 to standard form using algebraic techniques such as distribution and eliminating fractions. Suitable for students in Grades 9-11.

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