Plot a line graph for the variables `p` and `q`, where `p` is four times `q` i.e., the equation is `p=4q`.
Using the graph, find the value of `(i)p`, when `q=6` and `(ii) q` when `p=20`.

Answer

To solve the problem step by step, we will first plot the line graph for the equation \( p = 4q \) and then use the graph to find the required values.

### Step 1: Create a Table of Values
We need to create a table of values for \( p \) and \( q \) based on the equation \( p = 4q \).

| \( q \) | \( p = 4q \) |
|---------|--------------|
| 1 | 4 |
| 2 | 8 |
| 3 | 12 |
| 4 | 16 |
| 5 | 20 |
| 6 | 24 |
| 7 | 28 |

### Step 2: Plot the Points on a Graph
Now, we will plot the points from our table on a graph. The x-axis will represent \( q \) and the y-axis will represent \( p \).

- Plot the point (1, 4)
- Plot the point (2, 8)
- Plot the point (3, 12)
- Plot the point (4, 16)
- Plot the point (5, 20)
- Plot the point (6, 24)
- Plot the point (7, 28)

### Step 3: Draw the Line
Once all the points are plotted, we will draw a straight line through these points. This line represents the equation \( p = 4q \).

### Step 4: Find \( p \) when \( q = 6 \)
To find the value of \( p \) when \( q = 6 \):
- Locate \( q = 6 \) on the x-axis.
- Move vertically to the line and then horizontally to the y-axis.
- The corresponding value of \( p \) is 24.

### Step 5: Find \( q \) when \( p = 20 \)
To find the value of \( q \) when \( p = 20 \):
- Locate \( p = 20 \) on the y-axis.
- Move horizontally to the line and then vertically down to the x-axis.
- The corresponding value of \( q \) is 5.

### Final Answers
(i) \( p = 24 \) when \( q = 6 \)
(ii) \( q = 5 \) when \( p = 20 \)

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