Draw the graph of the equation `x+2y-3=0`.
From your graph, find the value for y when (i) x=5 (ii) x=-5.

Answer

To solve the problem of drawing the graph of the equation \(x + 2y - 3 = 0\) and finding the values of \(y\) for given \(x\) values, we will follow these steps:

### Step 1: Rewrite the equation
We start with the equation:
\[ x + 2y - 3 = 0 \]
We can rearrange this to express \(y\) in terms of \(x\):
\[ 2y = 3 - x \]
\[ y = \frac{3 - x}{2} \]

### Step 2: Find points for the graph
To draw the graph, we need at least two points. We can find these by substituting values for \(x\).

#### Point 1: When \(x = 0\)
Substituting \(x = 0\) into the equation:
\[ y = \frac{3 - 0}{2} = \frac{3}{2} = 1.5 \]
So, the first point is \((0, 1.5)\).

#### Point 2: When \(y = 0\)
Substituting \(y = 0\) into the equation:
\[ 0 = \frac{3 - x}{2} \]
This implies:
\[ 3 - x = 0 \implies x = 3 \]
So, the second point is \((3, 0)\).

### Step 3: Plot the points
Now we have two points: \((0, 1.5)\) and \((3, 0)\). We can plot these points on a graph.

### Step 4: Draw the line
Draw a straight line through the points \((0, 1.5)\) and \((3, 0)\). This line represents the equation \(x + 2y - 3 = 0\).

### Step 5: Find \(y\) when \(x = 5\)
To find \(y\) when \(x = 5\), substitute \(x = 5\) into the equation:
\[ y = \frac{3 - 5}{2} = \frac{-2}{2} = -1 \]
So, when \(x = 5\), \(y = -1\).

### Step 6: Find \(y\) when \(x = -5\)
To find \(y\) when \(x = -5\), substitute \(x = -5\) into the equation:
\[ y = \frac{3 - (-5)}{2} = \frac{3 + 5}{2} = \frac{8}{2} = 4 \]
So, when \(x = -5\), \(y = 4\).

### Summary of Results
- The graph of the equation \(x + 2y - 3 = 0\) is a straight line passing through the points \((0, 1.5)\) and \((3, 0)\).
- The value of \(y\) when \(x = 5\) is \(-1\).
- The value of \(y\) when \(x = -5\) is \(4\).