Rewrite the following equation in standard form.



*y* = 2*x* + 6

To rewrite the equation \( y = 2x + 6 \) in standard form, you need to express it as \( Ax + By = C \), where \( A \), \( B \), and \( C \) are integers, and \( A \) is non-negative.

Start with the given equation:

\[
y = 2x + 6
\]

Subtract \( 2x \) from both sides to move the \( x \) term to the left side:

\[
-2x + y = 6
\]

To make the coefficient of \( x \) positive, multiply the entire equation by \(-1\):

\[
2x - y = -6
\]

So, the equation in standard form is:

\[
2x - y = -6
\]

Do you have any questions or need further details? Here are some related questions:

1. How can you convert the standard form back to slope-intercept form?
2. Why is it important to have the coefficient of \( x \) as a positive integer in standard form?
3. How do you graph a line given its equation in standard form?
4. What is the difference between standard form and slope-intercept form?
5. How can you determine the intercepts of a line from its standard form equation?

**Tip:** Always check that the coefficients in the standard form equation are the smallest possible integers that maintain the same relationship.

Learn how to rewrite the equation y = 2x + 6 into standard form Ax + By = C. This problem covers linear equations and standard form concepts, with a step-by-step solution provided.

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