Draw the graph of equation `3x-4y=12`
Use the graph drawn to find:
(i) `y_(1)`, the value of y, when x=4
(ii) `y_(2)` the value of y, when x=0

Answer

To solve the equation \(3x - 4y = 12\) and draw its graph, we will follow these steps:

### Step 1: Rewrite the equation in slope-intercept form
We start with the equation:
\[ 3x - 4y = 12 \]
We need to isolate \(y\). First, we can subtract \(3x\) from both sides:
\[ -4y = -3x + 12 \]
Now, divide every term by \(-4\):
\[ y = \frac{3}{4}x - 3 \]

### Step 2: Identify points to plot
To draw the graph, we can choose values for \(x\) and calculate the corresponding \(y\) values. Let's choose \(x = 0\), \(x = 4\), and \(x = 1\).

1. **When \(x = 0\)**:
\[ y = \frac{3}{4}(0) - 3 = -3 \]
So, the point is \((0, -3)\).

2. **When \(x = 4\)**:
\[ y = \frac{3}{4}(4) - 3 = 3 - 3 = 0 \]
So, the point is \((4, 0)\).

3. **When \(x = 1\)**:
\[ y = \frac{3}{4}(1) - 3 = \frac{3}{4} - 3 = \frac{3}{4} - \frac{12}{4} = -\frac{9}{4} \approx -2.25 \]
So, the point is \((1, -2.25)\).

### Step 3: Plot the points
Now we can plot the points \((0, -3)\), \((4, 0)\), and \((1, -2.25)\) on a graph.

### Step 4: Draw the line
Connect the points with a straight line, which represents the equation \(3x - 4y = 12\).

### Step 5: Find \(y_1\) and \(y_2\)
Now, we can find the required values:

(i) **Finding \(y_1\) when \(x = 4\)**:
From our calculation, we found that when \(x = 4\), \(y = 0\). Thus, \(y_1 = 0\).

(ii) **Finding \(y_2\) when \(x = 0\)**:
From our calculation, we found that when \(x = 0\), \(y = -3\). Thus, \(y_2 = -3\).

### Final Answer:
- \(y_1 = 0\) when \(x = 4\)
- \(y_2 = -3\) when \(x = 0\)