Final answer:
The question requires solving for k in the slope formula. After computing, the result is k = 15, which does not match any of the provided options, suggesting a potential error in the question or options.
Step-by-step explanation:
To determine the value of k so that the slope of the line through the points (3,9) and (k,18) is 0.75, we use the slope formula: m = (y2 - y1) / (x2 - x1). We have m = 0.75, y2 = 18, y1 = 9, x2 = k, and x1 = 3. Plugging these values into the formula gives us:
0.75 = (18 - 9) / (k - 3)
0.75 = 9 / (k - 3)
To find k, multiply both sides by (k - 3) and then divide by 0.75:
k - 3 = 9 / 0.75
k - 3 = 12
k = 12 + 3
k = 15
However, since 15 is not one of the options, this suggests that there might have been an error in either the provided options or in the interpretation of the question.