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!