To solve the equation $20x - 8y = 40$, let's first simplify it.

Step-by-Step Solution

1. Simplify the equation:

   Divide every term by 4: $\frac{20x}{4} - \frac{8y}{4} = \frac{40}{4}$ $5x - 2y = 10$

2. Rearrange to the standard form $y = mx + b$ if needed:

   Let's solve for $y$: $5x - 2y = 10$ Subtract $5x$ from both sides: $-2y = -5x + 10$ Divide by $-2$: $y = \frac{5}{2}x - 5$

Interpreting the Result

• The equation in simplified form is $5x - 2y = 10$.
• In slope-intercept form, the equation is $y = \frac{5}{2}x - 5$.

Questions for Further Exploration

1. What are the x-intercept and y-intercept of the equation $5x - 2y = 10$?
2. How would you graph the equation $5x - 2y = 10$ on a coordinate plane?
3. What are the implications of the slope $\frac{5}{2}$ in the context of this line?
4. How can this equation be used in a real-world scenario or application?
5. What are the solutions for $x$ and $y$ if $y = 0$?

Tip

When dealing with linear equations, converting them to slope-intercept form ($y = mx + b$) can make it easier to graph and understand the relationship between $x$ and $y$.