The given equation is:

\[
4x - 5y = 20
\]

To explore this, we can approach it in different ways depending on what you're looking for. Here are a few possible ways to work with the equation:

### 1. Solving for \( y \) in terms of \( x \):
We can solve for \( y \) to express it as a function of \( x \):

\[
4x - 5y = 20
\]
Subtract \( 4x \) from both sides:
\[
-5y = -4x + 20
\]
Now, divide by \( -5 \):
\[
y = \frac{4x - 20}{5}
\]
This simplifies to:
\[
y = \frac{4}{5}x - 4
\]

### 2. Solving for \( x \) in terms of \( y \):
Alternatively, we can solve for \( x \):

\[
4x - 5y = 20
\]
Add \( 5y \) to both sides:
\[
4x = 5y + 20
\]
Now, divide by 4:
\[
x = \frac{5y + 20}{4}
\]
This simplifies to:
\[
x = \frac{5}{4}y + 5
\]

### 3. Finding intercepts:
- **x-intercept**: Set \( y = 0 \) in the equation:
  \[
  4x = 20 \implies x = 5
  \]
  The x-intercept is \( (5, 0) \).

- **y-intercept**: Set \( x = 0 \) in the equation:
  \[
  -5y = 20 \implies y = -4
  \]
  The y-intercept is \( (0, -4) \).

Would you like any further details or clarification on this?

Here are 5 related questions to deepen understanding:
1. How would the graph of this equation look like?
2. Can you find the slope and y-intercept of the line?
3. How would the equation change if it was \( 4x - 5y = 30 \)?
4. What happens to the equation when both \( x \) and \( y \) are doubled?
5. Can you find the point where the line crosses \( y = 2 \)?

**Tip**: Remember, solving linear equations often involves rearranging terms to isolate variables, which is a key algebraic skill!

Learn how to solve the linear equation 4x - 5y = 20 by expressing y in terms of x, finding the intercepts, and exploring key algebraic concepts. Suitable for students in Grades 8-10, this solution covers linear equations, slope-intercept form, and intercepts.

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