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Let's go through the questions one by one.

### Question 1: Write the rule for these graphs.
This question asks for the rules (equations) for four different graphs.

#### Graph (a):
- The graph shows a straight line passing through the origin (0, 0) and sloping downward. This is a straight line, and the slope seems to be negative.
- The equation should be of the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
- Since the line passes through the origin, \( b = 0 \), and the slope appears to be \( -1 \), meaning the rule for this graph is: 
  \[
  y = -x
  \]

#### Graph (b):
- This graph shows a straight line with a positive slope passing through the origin (0, 0).
- The slope looks to be positive and the same steepness as in part (a), suggesting the slope is 1.
- The rule is: 
  \[
  y = x
  \]

#### Graph (c):
- This graph is a horizontal line passing through \( y = 2 \) on the y-axis.
- A horizontal line has no slope, so the equation is just the y-value.
- The rule is: 
  \[
  y = 2
  \]

#### Graph (d):
- This graph is a vertical line passing through \( x = -3 \) on the x-axis.
- A vertical line has an undefined slope, and the equation is based on the x-value.
- The rule is: 
  \[
  x = -3
  \]

### Question 2: Sketch the following graphs.

#### Part (a): \( y = -1.5 \)
- This is a horizontal line where \( y \) is always \( -1.5 \).
- The graph will be a horizontal line crossing the y-axis at \( y = -1.5 \).

#### Part (b): \( x = 0 \)
- This is a vertical line where \( x \) is always \( 0 \), which is the y-axis.
- The graph will be a vertical line along the y-axis.

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Would you like more details or have any questions on these answers? 

Here are 5 related questions you could explore:
1. How can you determine the slope of a line from a graph?
2. What is the general equation of a line, and how do you find the slope?
3. How would the graph change if the slope in part (a) of Question 1 was steeper?
4. What is the significance of horizontal and vertical lines in geometry?
5. How do you interpret the intercepts of a line in relation to its graph?

**Tip**: For vertical lines, the equation will always be \( x = \text{{constant}} \), while for horizontal lines, it will always be \( y = \text{{constant}} \).

Write the rule for these graphs and sketch the following graphs: y = -1.5 and x = 0.

This problem focuses on identifying graph rules for linear functions, including horizontal and vertical lines, and understanding how to sketch these graphs. Suitable for students in Grades 8-10, it covers concepts like slope, intercepts, and graphing linear equations.

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