https://file.aiquickdraw.com/mathbot/file/1728945962021v94w1dsj.jpg

Let's go through the questions one by one based on the image you uploaded. I'll provide the solutions in detail.

### Questions 1-5 (Based on the first graph):

1. **What are the coordinates of point B?**
   - **Answer:** To find the coordinates of point B, locate it on the graph. It appears to be at (4, -2).

2. **What point is on the x-axis?**
   - **Answer:** A point on the x-axis will have a y-coordinate of 0. From the graph, point D seems to be on the x-axis at (2, 0).

3. **At what quadrant or axis is point C located?**
   - **Answer:** Point C is in the third quadrant since both its x and y coordinates are negative. Its approximate location is (-3, -4).

4. **What is the gradient of line AE?**
   - **Answer:** To find the gradient (slope) of line AE, use the formula:
     \[
     \text{Gradient} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
     \]
     For points A (6, 3) and E (0, -1):
     \[
     \text{Gradient} = \frac{3 - (-1)}{6 - 0} = \frac{4}{6} = \frac{2}{3}
     \]
     So, the gradient is \(\frac{2}{3}\).

5. **What is the gradient of the line parallel to the x-axis?**
   - **Answer:** A line parallel to the x-axis has a gradient (slope) of 0, because there is no change in the y-value as x changes.

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### Questions 6-11 (Based on the second graph and equation):

6. **What is the value of \( y \) when \( x = 3 \)?**
   - **Answer:** Using the equation \( y = 3x - 5 \):
     \[
     y = 3(3) - 5 = 9 - 5 = 4
     \]
     So, \( y = 4 \) when \( x = 3 \).

7. **What is the gradient of the line?**
   - **Answer:** The given equation is \( y = 3x - 5 \). The coefficient of \( x \) (which is 3) is the gradient of the line. Thus, the gradient is 3.

8. **At what value of \( y \) does the line intersect the y-axis?**
   - **Answer:** The y-intercept occurs when \( x = 0 \). Substituting into the equation:
     \[
     y = 3(0) - 5 = -5
     \]
     So, the line intersects the y-axis at \( y = -5 \).

9. **At what value of \( x \) does the line intersect the x-axis?**
   - **Answer:** The x-intercept occurs when \( y = 0 \). Set \( y = 0 \) in the equation:
     \[
     0 = 3x - 5 \implies 3x = 5 \implies x = \frac{5}{3}
     \]
     So, the line intersects the x-axis at \( x = \frac{5}{3} \).

10. **Which of the axes will the graph of the line \( y = -3 \) be parallel to?**
    - **Answer:** The line \( y = -3 \) is a horizontal line, meaning it is parallel to the x-axis.

11. **What is the equation of the line whose gradient is \( \frac{1}{2} \) and y-intercept is at \( -3 \)?**
    - **Answer:** The equation of a line is given by:
      \[
      y = mx + c
      \]
      where \( m \) is the gradient and \( c \) is the y-intercept. Substituting \( m = \frac{1}{2} \) and \( c = -3 \):
      \[
      y = \frac{1}{2}x - 3
      \]
      So, the equation of the line is \( y = \frac{1}{2}x - 3 \).

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Let me know if you'd like more details or clarifications on any of these questions. 

Here are 5 follow-up questions based on the above:
1. What is the significance of the gradient of a line in geometry?
2. How can you determine if two lines are parallel by comparing their gradients?
3. What is the general equation of a line, and what do its components represent?
4. How do you calculate the x-intercept and y-intercept of a linear equation?
5. What is the relationship between horizontal lines and their gradients?

**Tip:** To quickly find intercepts from a linear equation in standard form, substitute \( x = 0 \) for the y-intercept and \( y = 0 \) for the x-intercept.

Explore solutions to coordinate geometry problems, including calculating coordinates, gradients, and intercepts for linear equations. Suitable for Grade 9 students, this lesson covers key concepts such as slopes, intercepts, and the equation of a line.

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