To convert the equation \( y = 2x + 5 \) into standard form, we want the equation in the form:

\[
Ax + By = C
\]

where \(A\), \(B\), and \(C\) are integers, and \(A\) is non-negative.

Starting with:

\[
y = 2x + 5
\]

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

\[
-2x + y = 5
\]

To follow the standard convention of having \(A\) as a positive integer, multiply the entire equation by \(-1\):

\[
2x - y = -5
\]

Thus, the equation in standard form is:

\[
2x - y = -5
\]

Would you like further details or have any questions?

Here are 5 related questions to explore:

1. How would you convert \(y = -3x + 7\) to standard form?
2. What are the differences between slope-intercept form and standard form?
3. Can you convert \(y = 2x^2 + 3x + 1\) into standard form?
4. How do you find the x- and y-intercepts from the standard form equation?
5. How does the value of \(A\) affect the slope of the line in standard form?

**Tip:** In standard form, the coefficients of \(x\) and \(y\) should ideally be integers, and it's common to make \(A\) positive.

Learn how to convert the linear equation y = 2x + 5 into standard form with a step-by-step explanation. This problem demonstrates how to rewrite linear equations from slope-intercept form to standard form (Ax + By = C) and explains key algebraic concepts. Ideal for students in Grades 8-10.

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