Final answer:
The slope of the line connecting the provided ordered pairs is positive, which is incompatible with options A and B that have a negative slope. Option D is the closest match, though it seems there might be a typo since no option exactly fits the slope and y-intercept derived from the points.
Step-by-step explanation:
To determine which equation represents the set of ordered pairs {(-3, -4.5), (-1, -3.5), (1, -2.5), (6, 0)}, we can calculate the slope of the line that connects these points. The slope (m) of a line through any two points (x1, y1) and (x2, y2) is given by the formula m = (y2 - y1) / (x2 - x1). Using the first two points (-3, -4.5) and (-1, -3.5), the slope is m = (-3.5 - (-4.5)) / (-1 - (-3)) = 1/2. This indicates a positive slope, eliminating options A and B which suggest a negative slope.
We can also determine the y-intercept (b) of the line to see which option fits. If we substitute x = 6 and y = 0 into the slope-intercept form y = mx + b, we get 0 = (1/2) * 6 + b. Solving for b, we find b = -3. Thus, the equation of the line is y = (1/2)x - 3, which is not listed among the options. However, the closest equation that holds for the y-intercept and positive slope is option D. y = 2x + 6.
Note that there may be a typo since no exact match is found among the options. It is important to double-check the question and the options for accuracy.