Final answer:
The line perpendicular to y = -(2/5)x - 1 with a slope of 5/2 passing through the point (-2, 1) is y = (5/2)x + 6. The provided options do not include this correct equation, suggesting a transcription error.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another given line, first recognize that the slope of the perpendicular line will be the negative reciprocal of the given line's slope. The given line has an equation of y = -(2/5)x - 1, so its slope is -2/5. The negative reciprocal of -2/5 is 5/2, which will be the slope of the perpendicular line.
We want our new line to pass through the point (-2, 1). Using the slope-point form of a line equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through, we can substitute our values in to get:
y - 1 = (5/2)(x - (-2))
Expanding this equation, we get:
y - 1 = (5/2)x + 5
Finally, adding 1 to both sides to solve for y, we find:
y = (5/2)x + 6
However, we are looking for an equation from the provided options that matches this form. The correct equation should have a slope of 5/2 and cross through the point (-2, 1). Looking at the options, we realize that none of them are correct, indicating a possible transcription error. If we were to adjust the y-intercept based on the given point, the correct equation would actually be y = (5/2)x + 6.