The equation of the line perpendicular to the y-axis that passes through the point (–5, 1) is y = 1. true or false.

That's true. 

If the line is perpendicular to the y-axis, then it's horizontal,
and parallel to the x-axis. 

Every point on the line has the same y-coordinate.  If the point  (-5, 1) 
is on the line, then all the points  (any number, 1) are also on it. 
The equation of the line is 
                                               [ y = 1 ] .

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