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To find the x- and y-intercepts of the equation \(5x + 2y = 20\), we’ll solve for each intercept separately:

### 1. Finding the x-intercept:
For the x-intercept, set \( y = 0 \) and solve for \( x \).
\[
5x + 2(0) = 20
\]
\[
5x = 20
\]
\[
x = \frac{20}{5} = 4
\]
So, the x-intercept is \( x = 4 \).

### 2. Finding the y-intercept:
For the y-intercept, set \( x = 0 \) and solve for \( y \).
\[
5(0) + 2y = 20
\]
\[
2y = 20
\]
\[
y = \frac{20}{2} = 10
\]
So, the y-intercept is \( y = 10 \).

### Final Answer:
- **x-intercept**: 4
- **y-intercept**: 10

Would you like additional details on the solution, or have any questions about it?

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Here are some related questions to explore this topic further:
1. What would the intercepts be if the equation was \(5x + 2y = 15\)?
2. How would you find intercepts if the equation involved a fraction, such as \( \frac{5}{2}x + y = 20\)?
3. How does changing the slope of the line affect the x- and y-intercepts?
4. Can you determine intercepts if the line equation is given in slope-intercept form, like \(y = mx + b\)?
5. How do x- and y-intercepts help in graphing a linear equation?

**Tip**: Setting \( y = 0 \) finds the x-intercept, while setting \( x = 0 \) finds the y-intercept. This is a quick way to check key points on a line.

Find the x- and y-intercepts of the graph of 5x + 2y = 20. State each answer as an integer or an improper fraction in simplest form.

Learn how to find the x- and y-intercepts of the linear equation 5x + 2y = 20, presented with step-by-step instructions. This lesson covers core algebraic techniques suitable for students in Grades 8-10.

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