Final answer:
The equation x + y = -8 does not represent a line that is tangent to both coordinate axes and also tangent to the line x = -8. It does intersect both axes, but at different points, not at the origin (0,0) as would be required for tangency to both axes.
Step-by-step explanation:
The question is about determining which equation represents a line that is tangent to both coordinate axes and also tangent to the line x = -8. The given equation in the question is x + y = -8, and we must assess whether this line satisfies the required conditions.
For a line to be tangent to the x-axis, it has to touch the x-axis at exactly one point. That means it has a y-intercept of (0, b) where b is any real number. Similarly, for a line to be tangent to the y-axis, it must have an x-intercept of (a, 0) where a is any real number. A line tangent to x = -8 is simply a vertical line at x = -8, which does not intersect with any other lines except at x = -8.
However, the line given by the equation x + y = -8 is not tangent to the axis because it crosses both the x and y axes at one point each, but those points are not the same as each other (it crosses the y-axis at the point (0, -8) and the x-axis at the point (-8, 0)). Therefore, it indeed intersects both axes but is not tangent to them. In order for a line to be tangent to both axes, it would have to intercept each axis exactly once at (0,0), which this line does not. Hence, the given equation does not represent a line that fulfills all the conditions stated in the question.