Draw the graph of the straight line given by the equation` 4x-3y+36=0`
Calculate the area of the triangle formed by the lines drawn and the co-ordinate axes.

Answer

To solve the problem, we will follow these steps:

### Step 1: Rewrite the equation in slope-intercept form
The given equation is:
\[ 4x - 3y + 36 = 0 \]
Rearranging this, we get:
\[ 3y = 4x + 36 \]
\[ y = \frac{4}{3}x + 12 \]

### Step 2: Find the x-intercept and y-intercept
To find the intercepts, we will set \( y = 0 \) for the x-intercept and \( x = 0 \) for the y-intercept.

**Finding the y-intercept:**
Set \( x = 0 \):
\[ y = \frac{4}{3}(0) + 12 = 12 \]
So, the y-intercept is \( (0, 12) \).

**Finding the x-intercept:**
Set \( y = 0 \):
\[ 0 = \frac{4}{3}x + 12 \]
\[ \frac{4}{3}x = -12 \]
\[ x = -12 \times \frac{3}{4} = -9 \]
So, the x-intercept is \( (-9, 0) \).

### Step 3: Plot the points and draw the line
We have the points \( (0, 12) \) and \( (-9, 0) \). Plot these points on the graph and draw a straight line through them.

### Step 4: Calculate the area of the triangle formed by the line and the axes
The triangle formed by the line and the coordinate axes has:
- Base = Length along the x-axis = 9 units (from \( (0, 0) \) to \( (-9, 0) \))
- Height = Length along the y-axis = 12 units (from \( (0, 0) \) to \( (0, 12) \))

The area \( A \) of a triangle is given by the formula:
\[ A = \frac{1}{2} \times \text{Base} \times \text{Height} \]
Substituting the values:
\[ A = \frac{1}{2} \times 9 \times 12 = \frac{1}{2} \times 108 = 54 \text{ square units} \]

### Final Answer:
The area of the triangle formed by the line and the coordinate axes is \( 54 \) square units.

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