Final answer:
The equation of the line perpendicular to 2x+5y=-21 passing through (-8,1) is y=5/2x+21. This is found by calculating the negative reciprocal of the given line's slope and then using the point-slope form to determine the equation.
Step-by-step explanation:
To find the equation of the line perpendicular to 2x+5y=-21 that passes through the point (-8,1), we need to first find the slope of the given line.
The original equation can be rewritten in slope-intercept form (y=mx+b) as y=-(2/5)x-21/5. The slope (m) of this line is -2/5. For a line to be perpendicular, its slope must be the negative reciprocal of the original slope. Therefore, the slope of the perpendicular line is 5/2.
Using the point-slope form of a line equation, y-y1=m(x-x1), where (x1, y1) is the point (-8, 1) and m is the slope 5/2, we can write:
y-1=5/2(x+8).
Simplifying and putting it in slope-intercept form y=mx+b, we get:
y=5/2x + 21.
Therefore, the correct equation for the line is y=5/2x+21.