Question

Draw the graph of the equation \(x + 2y = 4\). Find the area of the triangle formed by the line intersecting the X-axis and Y-axis.

Hint:

For a line \(ax + by = c\), the intercepts are \(x = \frac{c}{a}\) and \(y = \frac{c}{b}\). The area of the triangle formed by the line with the coordinate axes is given by \[ \text{Area} = \frac{1}{2} \times x\text{-intercept} \times y\text{-intercept.} \]

Answer 1

Step 1: Find the intercepts.
Given equation: \[ x + 2y = 4 \] To find the X-intercept, put \(y = 0\): \[ x = 4 \] Hence, the X-intercept is \((4, 0)\). To find the Y-intercept, put \(x = 0\): \[ 2y = 4 \implies y = 2 \] Hence, the Y-intercept is \((0, 2)\).
Step 2: Plot the graph.
Plot the points \((4, 0)\) and \((0, 2)\) on a graph paper and draw a straight line joining them.
This line intersects the X-axis at \((4, 0)\) and the Y-axis at \((0, 2)\).
Step 3: Find the area of the triangle.
The line forms a right-angled triangle with the coordinate axes. Base = 4 units, Height = 2 units. \[ \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} \] \[ \text{Area} = \frac{1}{2} \times 4 \times 2 = 4 \text{ sq. units.} \] Step 4: Conclusion.
Hence, the area of the triangle formed by the line and the coordinate axes is \(4\) square units.
Final Answer: \[ \boxed{\text{Area = 4 square units}} \]