An equation is shown.


y−3=4(x−2)

 

Which of the following shows the equation written in standard form? 

	
−4x+y=3

	
−4x+y=1

	
−4x+y=−5

	
−4x+y=−11

 

We start with the given equation:

\[
y - 3 = 4(x - 2)
\]

### Step 1: Expand the equation

Expand the right-hand side:

\[
y - 3 = 4x - 8
\]

### Step 2: Isolate the \(y\)-term

Add 3 to both sides to get \(y\) by itself:

\[
y = 4x - 8 + 3
\]
\[
y = 4x - 5
\]

### Step 3: Rearrange to standard form

To write the equation in standard form \(Ax + By = C\), move the \(4x\) to the left-hand side by subtracting \(4x\) from both sides:

\[
-4x + y = -5
\]

### Final Equation:

\[
-4x + y = -5
\]

The correct option is:

\[
\boxed{-4x + y = -5}
\]

Would you like further details or have any questions? 

Here are 5 related questions to extend your understanding:

1. How would you convert an equation to slope-intercept form?
2. What does the slope represent in the equation \(y = mx + b\)?
3. How do you determine the x- and y-intercepts of a linear equation?
4. How can you solve systems of equations using substitution or elimination?
5. What is the geometric interpretation of a linear equation in two variables?

**Tip:** Standard form of a linear equation is typically written as \(Ax + By = C\), where \(A\), \(B\), and \(C\) are integers and \(A\) should ideally be positive.

An equation is shown. y−3=4(x−2) Which of the following shows the equation written in standard form? −4x+y=3 −4x+y=1 −4x+y=−5 −4x+y=−11

Learn how to convert the equation y−3=4(x−2) into standard form using algebraic methods. This example walks through expanding, isolating terms, and rearranging the equation into the standard form Ax + By = C. Suitable for students in Grades 8-10.

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