Use graph paper for this question. Take 1 cm = 1 unit on both axes.
(i) Draw the graphs of 𝑥 + 𝑦 + 3 = 0 𝑎𝑛𝑑 3𝑥 − 2𝑦 + 4 = 0. Plot three points per line.
(ii) Write down the coordinates of the point of intersection of the lines.

### To solve the given problem and draw the required graphs:

1. **Equation 1**: \(x + y + 3 = 0\) can be rearranged to:
   \[
   y = -x - 3
   \]
2. **Equation 2**: \(3x - 2y + 4 = 0\) can be rearranged to:
   \[
   y = \frac{3}{2}x + 2
   \]

### Part (i) – Plotting the Graphs:

#### 1. **For the first equation** \(y = -x - 3\):
We need three points to plot the graph. Choosing different values for \(x\):

- When \(x = 0\), \(y = -3\) → Point (0, -3)
- When \(x = -1\), \(y = -2\) → Point (-1, -2)
- When \(x = 1\), \(y = -4\) → Point (1, -4)

#### 2. **For the second equation** \(y = \frac{3}{2}x + 2\):
We also need three points to plot the graph. Again, choosing values for \(x\):

- When \(x = 0\), \(y = 2\) → Point (0, 2)
- When \(x = -2\), \(y = -1\) → Point (-2, -1)
- When \(x = 2\), \(y = 5\) → Point (2, 5)

### Part (ii) – Finding the Intersection Point:

We can solve these two equations algebraically by setting the expressions for \(y\) equal to each other:
\[
-x - 3 = \frac{3}{2}x + 2
\]
Now solve for \(x\):

- Multiply the entire equation by 2 to eliminate the fraction:
  \[
  -2x - 6 = 3x + 4
  \]
- Bring all \(x\)-terms to one side:
  \[
  -2x - 3x = 4 + 6
  \]
  \[
  -5x = 10 \quad \Rightarrow \quad x = -2
  \]

Now substitute \(x = -2\) into one of the original equations to find \(y\):
- Using \(y = -x - 3\):
  \[
  y = -(-2) - 3 = 2 - 3 = -1
  \]

So, the coordinates of the intersection point are **(-2, -1)**.

---

### Summary:

- **Intersection point**: (-2, -1)

Would you like more details or have any questions about this solution?

#### Relative questions:
1. How do you find the slope of a line from its equation?
2. What are other methods to solve a system of linear equations?
3. Can a system of two linear equations have more than one solution?
4. What is the geometric interpretation of parallel and intersecting lines?
5. How does the slope influence the steepness of a line?

#### Tip:
To quickly find the intersection of two lines graphically, ensure both lines are plotted with accurate scales and then visually locate the crossing point.

Use graph paper for this question. Take 1 cm = 1 unit on both axes. (i) Draw the graphs of 𝑥 + 𝑦 + 3 = 0 and 3𝑥 − 2𝑦 + 4 = 0. Plot three points per line. (ii) Write down the coordinates of the point of intersection of the lines.

Learn how to graph linear equations and find the intersection of x + y + 3 = 0 and 3x - 2y + 4 = 0. This problem includes key algebraic concepts, such as graphing in slope-intercept form and solving systems of linear equations. Suitable for students in Grades 8-10.

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