To solve the equation \(20x - 8y = 40\), we can rewrite it in different forms depending on what you're looking for. Here are some approaches:

### 1. Solving for \(y\) in terms of \(x\)
We can isolate \(y\) to express it in terms of \(x\):
\[
20x - 8y = 40
\]
Subtract \(20x\) from both sides:
\[
-8y = -20x + 40
\]
Now, divide by \(-8\):
\[
y = \frac{20x - 40}{8}
\]
Simplify:
\[
y = \frac{5x - 10}{2}
\]
So, the equation in slope-intercept form is:
\[
y = \frac{5}{2}x - 5
\]

### 2. Solving for \(x\) in terms of \(y\)
Alternatively, we can solve for \(x\) in terms of \(y\):
\[
20x - 8y = 40
\]
Add \(8y\) to both sides:
\[
20x = 8y + 40
\]
Now, divide by 20:
\[
x = \frac{8y + 40}{20}
\]
Simplify:
\[
x = \frac{2y + 10}{5}
\]

### 3. Finding the intercepts
- **x-intercept**: Set \(y = 0\), then solve for \(x\):
  \[
  20x - 8(0) = 40 \implies 20x = 40 \implies x = 2
  \]
  So, the x-intercept is \( (2, 0) \).

- **y-intercept**: Set \(x = 0\), then solve for \(y\):
  \[
  20(0) - 8y = 40 \implies -8y = 40 \implies y = -5
  \]
  So, the y-intercept is \( (0, -5) \).

Would you like a more detailed explanation, or do you have any questions?

### Related Questions
1. How do you convert a linear equation into standard form?
2. What are the steps to graph a linear equation?
3. How do you find the slope and intercepts of a line from an equation?
4. Can you explain how to solve a system of linear equations?
5. How do you use the slope-intercept form to graph a line?

### Tip:
When graphing a linear equation, always find the x- and y-intercepts first. They provide two points to draw the line accurately.

Discover how to solve the linear equation 20x−8y=40, convert it to slope-intercept form, and find the x- and y-intercepts. This detailed solution covers key algebra concepts suitable for Grades 8-10.

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