Final Answer:
The equation in slope-intercept form for the line that includes side CD of the rhombus-shaped building is **A) y = -11x + 10**.
Step-by-step explanation:
Side AB of the rhombus passes through point (6,6) and is perpendicular to the line y = -11. This implies that the slope of side AB is the negative reciprocal of the slope of the line y = -11, which is 1/11. Therefore, the slope of side AB is -11 (negative reciprocal of 1/11). Since side CD is parallel to side AB, it will have the same slope of -11.
To find the equation of the line passing through point (-6,10) with a slope of -11, we use the point-slope form of a line, which is y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope. Substituting (-6,10) for (x₁, y₁) and -11 for the slope m, we get y - 10 = -11(x - (-6)). Simplifying this equation gives y - 10 = -11(x + 6), and further simplification results in y = -11x - 66 + 10, which simplifies to y = -11x + 10.
Therefore, the equation in slope-intercept form for the line that includes side CD of the rhombus-shaped building is y = -11x + 10, as it passes through the given point (-6,10) and has a slope of -11, which is parallel to side AB.