Final answer:
The area under the curve y = 8 - x for x ≥ 2 is the area of a right triangle with a base and height of 6. The calculated area is ½ × base × height = ½ × 6 × 6 = 18, which is not reflected in any of the provided answer options.
Step-by-step explanation:
To find the area under the curve y = 8 - x for x ≥ 2, we need to consider the graphical representation of this function. It's a linear function with a negative slope that intersects the y-axis at y = 8. Since the question is asking about the area for x ≥ 2, we visualize this area as a right triangle with the line y = 8 - x as the hypotenuse, the x-axis as the base, and the line x = 2 as the height.
At x = 2, the height of the triangle can be found by plugging the value into the equation of the line: y = 8 - 2 = 6. To find the base, we consider the intercepts: the triangle will extend to the x-axis, where y = 0, which happens at x = 8. So the width of the base is 8 - 2 = 6. Therefore, the area of the triangle can be calculated as:
½ × base × height
½ × 6 × 6 = 18
Hence, none of the given options is the correct answer for the area under the curve y = 8 - x for x ≥ 2.