Final answer:
The slope of the line perpendicular to y = -2/5x - 1 is 5/2. Using the point (-2,14) and the point-slope formula, the correct equation is y = (5/2)x + 19. However, this is not one of the given options, indicating a discrepancy in the provided choices.
Step-by-step explanation:
To find the equation of a line perpendicular to the given line y = -2/5x - 1, we first determine the slope of the perpendicular line. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of our line will be the negative reciprocal of -2/5, which is 5/2.
Using the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we plug in the slope 5/2 and the given point (-2, 14):
y - 14 = (5/2)(x - (-2))
Simplifying this equation:
y - 14 = (5/2)x + 5
Add 14 to both sides:
y = (5/2)x + 19
However, none of the answer choices matches this equation exactly. There may be an error in the provided answer choices, as the correct answer, based on the given point and perpendicular slope, is not listed. The closest match with respect to the slope is option b) y = 5/2x - 10, but the y-intercept is incorrect.