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 \(y\).

Discover how to solve the linear equation 20x - 8y = 40 with a step-by-step breakdown, simplifying it and converting it to slope-intercept form (y = mx + b). Perfect for Grades 8-10 students learning about algebra and linear equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation