The required equation of line B is 2y+5x=-2
The equation of a line in point-slope form is expressed as:
y-y0 = m(x-x0)
m is the slope of the line
(x0, y0) is the point on the line
Given the line A expressed as:
2x = 5y – 25
Rewrite in standard form
5y = 2x + 25
y = 2/5 x + 5
The slope will be 2/5
The slope of the perpendicular line will be;
[tex]M = \frac{-1}{(2/5)}\\M = \frac{-5}{2}[/tex]
Substitute the point (-6, 14) and slope -5/2 into the equation above to get the required equation of line B
[tex]y-14=-5/2(x+6)\\2(y-14) = -5(x+6)\\2y-28=-5x-30\\2y+5x=-30+28\\2y+5x=-2\\[/tex]
Hence the required equation of line B is 2y+5x=-2
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