https://file.aiquickdraw.com/mathbot/file/17273516364494m4j6q4p.jpg

Let's analyze the graph and the questions provided.

### Features of Line A
From the graph:
- Line A passes through points \( (0, 6) \) and \( (6, 0) \). Using these two points, we can determine the slope (gradient) and intercepts.

#### Gradient of Line A:
The formula for the gradient between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
For Line A:
- \( (x_1, y_1) = (0, 6) \)
- \( (x_2, y_2) = (6, 0) \)
\[
m_A = \frac{0 - 6}{6 - 0} = \frac{-6}{6} = -1
\]

#### Intercepts of Line A:
- **y-intercept**: The line crosses the y-axis at \( y = 6 \), so the y-intercept is \( 6 \).
- **x-intercept**: The line crosses the x-axis at \( x = 6 \), so the x-intercept is \( 6 \).

### Features of Line B
From the graph:
- Line B passes through points \( (6, 0) \) and \( (0, -6) \). Using these two points, we can calculate the slope and intercepts.

#### Gradient of Line B:
Using the same formula:
\[
m_B = \frac{-6 - 0}{0 - 6} = \frac{-6}{-6} = 1
\]

#### Intercepts of Line B:
- **y-intercept**: The line crosses the y-axis at \( y = -6 \), so the y-intercept is \( -6 \).
- **x-intercept**: The line crosses the x-axis at \( x = 6 \), so the x-intercept is \( 6 \).

### Features of the line \( y + 7x = 42 \)

We need to rewrite this equation in slope-intercept form \( y = mx + b \), where \( m \) is the slope, and \( b \) is the y-intercept.

Rearrange \( y + 7x = 42 \):
\[
y = -7x + 42
\]

#### x- and y-intercepts:
- **y-intercept**: The y-intercept is \( 42 \) (when \( x = 0 \)).
- **x-intercept**: To find the x-intercept, set \( y = 0 \) and solve for \( x \):
\[
0 = -7x + 42 \quad \Rightarrow \quad 7x = 42 \quad \Rightarrow \quad x = 6
\]

### Final Answers:
- **Line A**:
  - Gradient: \( -1 \)
  - \( x \)-intercept: \( 6 \)
  - \( y \)-intercept: \( 6 \)
  
- **Line B**:
  - Gradient: \( 1 \)
  - \( x \)-intercept: \( 6 \)
  - \( y \)-intercept: \( -6 \)
  
- **For \( y + 7x = 42 \)**:
  - \( x \)-intercept: \( 6 \)
  - \( y \)-intercept: \( 42 \)

Would you like further details or clarifications?

### 5 Related Questions:
1. How do you find the equation of a line given two points?
2. What is the general form of a linear equation, and how does it relate to slope-intercept form?
3. How can you calculate the slope of a line parallel to a given line?
4. How do vertical and horizontal lines differ in terms of slope and intercepts?
5. How do the slopes of perpendicular lines relate to each other?

### Tip:
Always remember that a negative slope means the line is decreasing from left to right, while a positive slope means it is increasing.

Find the features of lines A and B, and the features of the line y + 7x = 42.

Learn how to determine the gradient and intercepts of lines A and B using the slope formula and how to analyze the line y + 7x = 42 by converting it into slope-intercept form. A perfect guide for students in Grades 8-10.

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