3.1 Draw neat graphs on Annexure $$ A $$ of a line through the points $$ P(-1: 0) $$ and $$ 3(1: 2) $$ and a line through the points $$ R(1: 4) $$ and $$ S(-1: 2) $$ 3.3 Wetermine the equations of the straight lines $$ P Q $$ and $$ R S $$ 3.4 Hence complete the statement __ lines have _ gradients.

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Let's solve the problem step by step.

### Step 1: Extract Known Conditions
We have two lines defined by the following points:
- Line $$ PQ $$ through points $$ P(-1, 0) $$ and $$ Q(3, 2) $$
- Line $$ RS $$ through points $$ R(1, 4) $$ and $$ S(-1, 2) $$

### Step 2: Determine the Equations of the Lines

#### 3.3: Find the equations of the straight lines $$ PQ $$ and $$ RS $$

**Finding the equation of line $$ PQ $$:**

1. **Calculate the slope $$ m $$ of line $$ PQ $$**:
   $$
   m_{PQ} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 0}{3 - (-1)} = \frac{2}{4} = \frac{1}{2}
   $$

2. **Use point-slope form to find the equation**:
   The point-slope form is given by:
   $$
   y - y_1 = m(x - x_1)
   $$
   Using point $$ P(-1, 0) $$:
   $$
   y - 0 = \frac{1}{2}(x - (-1)) \implies y = \frac{1}{2}(x + 1) \implies y = \frac{1}{2}x + \frac{1}{2}
   $$

**Finding the equation of line $$ RS $$:**

1. **Calculate the slope $$ m $$ of line $$ RS $$**:
   $$
   m_{RS} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 4}{-1 - 1} = \frac{-2}{-2} = 1
   $$

2. **Use point-slope form to find the equation**:
   Using point $$ R(1, 4) $$:
   $$
   y - 4 = 1(x - 1) \implies y - 4 = x - 1 \implies y = x + 3
   $$

### Step 3: Complete the Statement

Now we have the equations of the lines:
- Line $$ PQ: y = \frac{1}{2}x + \frac{1}{2} $$
- Line $$ RS: y = x + 3 $$

**Gradients:**
- The gradient of line $$ PQ $$ is $$ \frac{1}{2} $$.
- The gradient of line $$ RS $$ is $$ 1 $$.

### Final Statement
Thus, we can complete the statement:
**"The lines have different gradients."**

### Step 4: Graphing the Lines
To graph the lines, we can plot the points and draw the lines through them. However, since I cannot draw directly here, I recommend using graphing software or graph paper to plot the points $$ P, Q, R, $$ and $$ S $$ and draw the lines based on the equations derived.

If you need further assistance with the graphing or any other part, feel free to ask!
The lines have different gradients.

3.1 Draw neat graphs on Annexure \( A \) of a line through the points \( P(-1: 0) \) and \( 3(1: 2) \) and a line through the points \( R(1: 4) \) and \( S(-1: 2) \) 3.3 Wetermine the equations of the straight lines \( P Q \) and \( R S \) 3.4 Hence complete the statement __ lines have _ gradients.

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