Draw the graph of the equation x+2y =4, use graph to find :
(a) `X_(1)`, the value of x when `y =4 (b) Y_(1)` the value of y when x= -2

Explanation

To solve the problem step by step, we will first rewrite the equation and then create a table of values to plot the graph of the equation \(x + 2y = 4\). After plotting the graph, we will find the required values.

### Step 1: Rewrite the Equation
We start with the equation:
\[ x + 2y = 4 \]
We can rearrange this equation to express \(x\) in terms of \(y\):
\[ x = 4 - 2y \]

### Step 2: Create a Table of Values
Next, we will create a table by substituting different values for \(y\) to find corresponding values of \(x\).

| \(y\) | \(x = 4 - 2y\) | Resulting \(x\) |
|-------|----------------|------------------|
| 0 | \(4 - 2(0)\) | 4 |
| 1 | \(4 - 2(1)\) | 2 |
| 2 | \(4 - 2(2)\) | 0 |
| 3 | \(4 - 2(3)\) | -2 |
| 4 | \(4 - 2(4)\) | -4 |
| 5 | \(4 - 2(5)\) | -6 |

### Step 3: Plot the Points on a Graph
Now we will plot the points from the table on a graph with the x-axis and y-axis.

- Points to plot:
- (4, 0)
- (2, 1)
- (0, 2)
- (-2, 3)
- (-4, 4)
- (-6, 5)

### Step 4: Draw the Line
After plotting the points, we will draw a straight line through these points, as they represent the linear equation \(x + 2y = 4\).

### Step 5: Find \(X_1\) when \(Y = 4\)
From the graph, we can see that when \(y = 4\), the corresponding value of \(x\) is:
\[ X_1 = -4 \]

### Step 6: Find \(Y_1\) when \(X = -2\)
Similarly, from the graph, when \(x = -2\), the corresponding value of \(y\) is:
\[ Y_1 = 3 \]

### Final Answers
(a) The value of \(X_1\) when \(Y = 4\) is \(-4\).

(b) The value of \(Y_1\) when \(X = -2\) is \(3\).

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