Final answer:
The area of the triangular region bounded by the coordinate axes and the line $2x + y = 6$ is calculated using the intercepts on the axes, resulting in an area of 9 square units.
Step-by-step explanation:
The student's question relates to calculating the area of a triangular region bounded by the coordinate axes and a given line. The line in question is $2x + y = 6$. To find the points where this line intersects the axes, we can set $y$ to 0 to find the $x$-intercept and $x$ to 0 to find the $y$-intercept.
This gives us the points (3, 0) for the $x$-intercept and (0, 6) for the $y$-intercept. Since the triangle is right-angled with these intercepts forming the base and height, the area of the triangular region is found by applying the formula for the area of a triangle, which is \(\frac{1}{2} \times \text{base} \times \text{height}\). Substituting the intercepts in, the area becomes \(\frac{1}{2} \times 3 \times 6 = 9\) square units.