Which line is perpendicular to y=-1/3x

Answer 1

just take the negative inverse of the x coefficient.

change the sign and flip it upside down. slope of y=(-1/3)x is -1/3

the perpendicular lines all have slope = +3

there's an infinite number of perpendicular lines

but the most simple might by y=3x, which intersects at the origin

still any line such as y=3x + b where b is any real number also is perpendicular

One little point remaining thous is the way the equation is written, it really reads y=-1/(3x) not y=(-1/3)x

but y=-1(3x) is not a line, it's a hyperbola, a rectangular hyperbola, with a variable slope

y' = (1/3)/x^2 = slope of the non-linear curve, not a line

a perpendicular line to the curve would depend on where on the curve you wanted the line to intersect, unlike a perpendicular to a straight line.

Answer 2

y = 3x+ c, where c is any real number, works. c = 0, or y = 3x, is the first example one can think of.