Final answer:
The area of a triangle bounded by the x-axis, y-axis, and the line y = -x + 8 is 32 square units. This is a right triangle with vertices at (0,0), (8,0), and (0,8), and the area is calculated as 1/2 × base × height.
Step-by-step explanation:
The student has asked what the area of the triangle bounded by the x-axis, the y-axis, and the line y = -x + 8 is. To find the area of this triangle, we can visualize it in the coordinate plane. The y-intercept of the line y = -x + 8 is at the point (0, 8), which means that the line crosses the y-axis at 8. The x-intercept is found by setting y to zero and solving for x, giving us x = 8. So the line crosses the x-axis at the point (8, 0). The triangle formed is a right triangle with the right angle at the origin (0,0), a base along the x-axis from (0,0) to (8,0), and a height along the y-axis from (0,0) to (0,8).
The area of a triangle is given by the formula Area = 1/2 × base × height. Substituting our base (8 units) and height (8 units), we get Area = 1/2 × 8 × 8 = 32 square units. Therefore, the area of the triangle is 32 square units.