https://file.aiquickdraw.com/mathbot/file/1727459069144btrmkt6s.jpg

Let's solve the given equations to find their **x**-intercepts and **y**-intercepts.

### a) \( 10x + 4y = 20 \)

- **x-intercept**: Set \( y = 0 \) and solve for \( x \).
  \[
  10x + 4(0) = 20 \implies 10x = 20 \implies x = 2
  \]
  The x-intercept is \( (2, 0) \).

- **y-intercept**: Set \( x = 0 \) and solve for \( y \).
  \[
  10(0) + 4y = 20 \implies 4y = 20 \implies y = 5
  \]
  The y-intercept is \( (0, 5) \).

### b) \( 4x - 8y = -40 \)

- **x-intercept**: Set \( y = 0 \) and solve for \( x \).
  \[
  4x - 8(0) = -40 \implies 4x = -40 \implies x = -10
  \]
  The x-intercept is \( (-10, 0) \).

- **y-intercept**: Set \( x = 0 \) and solve for \( y \).
  \[
  4(0) - 8y = -40 \implies -8y = -40 \implies y = 5
  \]
  The y-intercept is \( (0, 5) \).

### c) \( x = -5 \)

This is a vertical line, so it only has an x-intercept.

- **x-intercept**: \( x = -5 \), so the intercept is \( (-5, 0) \).
- **y-intercept**: Since it's a vertical line, there is no y-intercept.

### d) \( y = 3 \)

This is a horizontal line, so it only has a y-intercept.

- **x-intercept**: A horizontal line has no x-intercept.
- **y-intercept**: \( y = 3 \), so the intercept is \( (0, 3) \).

### Summary of the intercepts:
a) x-int: \( 2 \), y-int: \( 5 \)  
b) x-int: \( -10 \), y-int: \( 5 \)  
c) x-int: \( -5 \), y-int: None  
d) x-int: None, y-int: \( 3 \)

Let me know if you need more details or if you have any questions!

Here are some additional related questions to consider:
1. How do you find intercepts for non-linear equations?
2. What does the slope of a line tell us about the relationship between x and y?
3. Can a line have both intercepts equal to zero? What does that mean geometrically?
4. What is the intercept form of the equation of a line?
5. How would intercepts change if the coefficients in the equation were fractions?

**Tip:** Always substitute \( x = 0 \) for y-intercepts and \( y = 0 \) for x-intercepts to solve these kinds of problems easily.

Identify the x and y intercepts of each equation: a) 10x + 4y = 20; b) 4x - 8y = -40; c) x = -5; d) y = 3

Learn how to find the x and y intercepts of linear equations such as 10x + 4y = 20, 4x - 8y = -40, x = -5, and y = 3. Detailed step-by-step solutions provided. Suitable for Grades 7-10.

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