https://file.aiquickdraw.com/mathbot/file/17265129057962sesbvaq.jpg

To solve these equations and sketch the graphs using intercepts, we'll calculate both the x- and y-intercepts for each equation. To do this:

- **x-intercept**: Set \( y = 0 \) and solve for \( x \).
- **y-intercept**: Set \( x = 0 \) and solve for \( y \).

### 1) \( x + 5y = 25 \)

- **x-intercept**: 
  \[
  x + 5(0) = 25 \implies x = 25
  \]
  The x-intercept is \( (25, 0) \).

- **y-intercept**:
  \[
  0 + 5y = 25 \implies y = 5
  \]
  The y-intercept is \( (0, 5) \).

### 2) \( 3x - 4y = 16 \)

- **x-intercept**: 
  \[
  3x - 4(0) = 16 \implies 3x = 16 \implies x = \frac{16}{3} \approx 5.33
  \]
  The x-intercept is \( \left( \frac{16}{3}, 0 \right) \).

- **y-intercept**:
  \[
  3(0) - 4y = 16 \implies -4y = 16 \implies y = -4
  \]
  The y-intercept is \( (0, -4) \).

### 3) \( 3x + y = -3 \)

- **x-intercept**: 
  \[
  3x + 0 = -3 \implies x = -1
  \]
  The x-intercept is \( (-1, 0) \).

- **y-intercept**:
  \[
  3(0) + y = -3 \implies y = -3
  \]
  The y-intercept is \( (0, -3) \).

### 4) \( 2x + y = -5 \)

- **x-intercept**: 
  \[
  2x + 0 = -5 \implies x = -\frac{5}{2} = -2.5
  \]
  The x-intercept is \( \left( -\frac{5}{2}, 0 \right) \).

- **y-intercept**:
  \[
  2(0) + y = -5 \implies y = -5
  \]
  The y-intercept is \( (0, -5) \).

### 5) \( 9x - 4y = -20 \)

- **x-intercept**: 
  \[
  9x - 4(0) = -20 \implies 9x = -20 \implies x = -\frac{20}{9} \approx -2.22
  \]
  The x-intercept is \( \left( -\frac{20}{9}, 0 \right) \).

- **y-intercept**:
  \[
  9(0) - 4y = -20 \implies -4y = -20 \implies y = 5
  \]
  The y-intercept is \( (0, 5) \).

---

### Summary of Intercepts:
1. \( x + 5y = 25 \) → x-intercept: \( (25, 0) \), y-intercept: \( (0, 5) \)
2. \( 3x - 4y = 16 \) → x-intercept: \( \left( \frac{16}{3}, 0 \right) \), y-intercept: \( (0, -4) \)
3. \( 3x + y = -3 \) → x-intercept: \( (-1, 0) \), y-intercept: \( (0, -3) \)
4. \( 2x + y = -5 \) → x-intercept: \( \left( -\frac{5}{2}, 0 \right) \), y-intercept: \( (0, -5) \)
5. \( 9x - 4y = -20 \) → x-intercept: \( \left( -\frac{20}{9}, 0 \right) \), y-intercept: \( (0, 5) \)

Would you like any specific details on graphing these, or further clarifications?

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### Relative questions:
1. How do you calculate the slope of each line from the intercepts?
2. Can you find the equation of a line perpendicular to one of these?
3. What happens if you rewrite these equations in slope-intercept form?
4. How do intercepts help in understanding the behavior of linear equations?
5. How would you find the intersection points of these lines?

### Tip: 
When using intercepts, plotting the points on a graph and drawing a line between them helps visualize how the equation behaves across different values of \( x \) and \( y \).

Sketch the graph of each line using intercepts. 1) x + 5y = 25, 2) 3x - 4y = 16, 3) 3x + y = -3, 4) 2x + y = -5, 5) 9x - 4y = -20

Learn how to graph linear equations like x + 5y = 25, 3x - 4y = 16, and others by finding the x and y intercepts. Suitable for students in Grades 8-10, this tutorial covers key concepts such as the intercept theorem and graphing techniques.

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