Draw the graph of the equation y=3x.
Form your graph, find the value of y when (i) x=2 (ii) x=-2.

Answer

To solve the problem of drawing the graph of the equation \( y = 3x \) and finding the values of \( y \) for specific \( x \) values, we will follow these steps:

### Step 1: Understand the Equation
The equation \( y = 3x \) represents a linear relationship between \( x \) and \( y \). For every unit increase in \( x \), \( y \) increases by 3 units.

### Step 2: Create a Table of Values
To draw the graph, we can create a table of values for \( x \) and \( y \):

| \( x \) | \( y = 3x \) |
|---------|--------------|
| 0 | 0 |
| 1 | 3 |
| 2 | 6 |
| -1 | -3 |
| -2 | -6 |

### Step 3: Plot the Points
Using the table, we can plot the points on a Cartesian plane:
- \( (0, 0) \)
- \( (1, 3) \)
- \( (2, 6) \)
- \( (-1, -3) \)
- \( (-2, -6) \)

### Step 4: Draw the Graph
After plotting the points, we can draw a straight line through them. The line will extend infinitely in both directions.

### Step 5: Find the Value of \( y \) when \( x = 2 \)
Using the equation \( y = 3x \):
- When \( x = 2 \):
\[ y = 3 \times 2 = 6 \]
So, the coordinate is \( (2, 6) \).

### Step 6: Find the Value of \( y \) when \( x = -2 \)
Using the equation \( y = 3x \):
- When \( x = -2 \):
\[ y = 3 \times (-2) = -6 \]
So, the coordinate is \( (-2, -6) \).

### Final Answer
- The value of \( y \) when \( x = 2 \) is \( 6 \).
- The value of \( y \) when \( x = -2 \) is \( -6 \).