Final answer:
Calculating the slope (0.6) and intercept (12.2) for the equation of the line passing through (-2, 11) and (3, 14) results in the equation y = 0.6x + 12.2, which does not match any of the provided choices. This indicates a possible error in the answer choices provided.
Step-by-step explanation:
To find the equation of the line in slope-intercept form that passes through the points (-2, 11) and (3, 14), we need to calculate the slope (m) and the y-intercept (b) of the line. The slope is the change in y divided by the change in x between two points on the line which can be calculated by using the formula:
m = (y2 - y1) / (x2 - x1)
Using this formula and our points (-2, 11) and (3, 14), the slope calculation would be:
m = (14 - 11) / (3 - (-2)) = 3 / 5 = 0.6
Now, we can use the slope and one of the given points in the point-slope form equation, y - y1 = m(x - x1), to solve for b. Let's use the point (-2, 11):
11 = 0.6(-2) + b
b = 11 + 1.2 = 12.2
The equation of the line in slope-intercept form is therefore y = 0.6x + 12.2, which does not match any of the provided answer choices (A to D). It appears there may have been a miscalculation in the question or in the creation of the answer choices. The correct procedure was followed, but none of the given options are correct based on the two points provided.