To solve the equation \( xy - 4x + 4 = 0 \), let's break it down step by step:

1. The equation is linear in \( y \) and involves \( x \) as well.
2. Isolate the term with \( y \) to solve for \( y \) in terms of \( x \).

### Step 1: Isolate \( y \)
\[
xy - 4x + 4 = 0
\]
First, subtract \( 4 \) from both sides:
\[
xy - 4x = -4
\]
Now, factor out \( x \) from the left-hand side:
\[
x(y - 4) = -4
\]
### Step 2: Solve for \( y \)
Now, divide both sides by \( x \) (assuming \( x \neq 0 \)):
\[
y - 4 = \frac{-4}{x}
\]
Finally, solve for \( y \):
\[
y = \frac{-4}{x} + 4
\]

Thus, the solution in terms of \( y \) is:
\[
y = 4 - \frac{4}{x}
\]

Would you like further details on this, or do you have any questions?

Here are 5 related questions to explore this further:
1. What happens if \( x = 0 \) in this equation?
2. How would you graph \( y = 4 - \frac{4}{x} \)?
3. Can you interpret the asymptotes of this function?
4. How can this equation be rearranged to find \( x \) in terms of \( y \)?
5. What happens to \( y \) as \( x \) approaches infinity?

**Tip:** When solving equations involving multiple variables, always try to isolate one variable at a time to simplify the problem.

Learn how to solve the linear equation xy - 4x + 4 = 0 with a step-by-step solution. This algebra problem involves factoring and solving for y in terms of x, providing a clear breakdown for high school students (Grades 9-12).

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