Final answer:
The equation of a curve passing through the point (0, 2) cannot be found given the given conditions.
Step-by-step explanation:
The equation of the curve passing through the point (0, 2) can be found using the given information. Let's assume the equation of the curve is y = f(x).
Given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5, we can write the equation as:
y + x = |f'(x)| + 5
Now, substituting the coordinates of the given point (0, 2), we have:
2 + 0 = |f'(0)| + 5
2 = |f'(0)| + 5
|f'(0)| = 2 - 5
|f'(0)| = -3
Since the magnitude of a slope cannot be negative, there is no solution that satisfies the given conditions. Therefore, there is no equation of a curve passing through the point (0, 2) that meets the given criteria.