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We are asked to rewrite the equation \( y = \frac{2}{5}x - 8 \) in standard form. Standard form for a linear equation is generally written as:

\[
Ax + By = C
\]

Where \( A \), \( B \), and \( C \) are integers, and \( A \) is usually positive.

Let's transform the given equation step by step:

### Step 1: Eliminate the fraction
Multiply both sides of the equation by 5 to eliminate the denominator:

\[
5y = 2x - 40
\]

### Step 2: Rearrange into standard form
Move the \( 2x \) term to the left-hand side to match the standard form:

\[
-2x + 5y = -40
\]

### Step 3: Adjust the sign of the equation
To make the coefficient of \( x \) positive, multiply the entire equation by \(-1\):

\[
2x - 5y = 40
\]

Now the equation is in standard form.

Thus, the blanks in the original problem should be filled as follows:

\[
2x + 5y = 40
\]

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Would you like further details or explanations on this transformation?

Here are 5 related questions to expand on this:

1. How would you convert an equation in point-slope form to standard form?
2. What does the standard form of a linear equation represent geometrically?
3. Can you derive the slope of a line from its standard form?
4. What are the advantages of writing a linear equation in standard form?
5. How do you convert from slope-intercept form to standard form when the slope is a negative fraction?

**Tip:** When working with linear equations, always check if your final standard form can be simplified or if coefficients can be adjusted to integers.

Rewrite y = (2/5)x - 8 in standard form by completing the equation.

Learn how to convert the linear equation y = (2/5)x - 8 to standard form using algebraic steps. This example covers key concepts in algebra, including eliminating fractions and rearranging equations. Suitable for students in Grades 8-10.

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