Plotting horizontal and vertical lines in Mathematica

Question

In Mathematica, how do you plot a horizontal line at a given number? How do you plot a vertical line at a given number?

Solution 1

If you're actually using Plot (or ListPlot, et c.), the easiest solution is to use the GridLines option, which lets you specify the x- and y-values where you want the lines drawn. For instance:

Plot[Sin[x], {x, 0, 2 \[Pi]},
  GridLines -> {{0, \[Pi]/2, \[Pi], 3 \[Pi]/2, 2 \[Pi]},
                {-1, -Sqrt[3]/2, -1/2, 0, 1/2, Sqrt[3]/2, 1}}]

EDIT to add:

Of course, this solution works if you just want to draw a line at a single, given number. For instance, if you want to reproduce the second example from dreeve's answer:

Plot[Sin[x], {x, 0, 2 Pi},
 GridLines -> {{4}, {}}]

Solution 2

For the case of horizontal lines when using Plot the easiest trick is to just include additional constant functions:

Plot[{Sin[x], .75}, {x, 0, 2Pi}]

For vertical lines, there's the Epilog option for Plot and ListPlot:

Plot[Sin[x], {x, 0, 2Pi}, Epilog->Line[{{4,-100}, {4,100}}]]

But probably the best is the GridLines option given in Pillsy's answer.

Solution 3

One approach would be to add Line graphic primitives to your graphics:

p1 = Plot[Sin[x], {x, -2*Pi,2*Pi}];
l1 = Graphics@Line[{{-2Pi,.75},{2Pi,.75}}]; (* horizontal line at y==.75 *)
Show[p1,l1]

Another approach would be to fiddle around with GridLines.

Solution 4

Use the Gridlines command like so:

Plot[
  1/(15*E^((x - 100)^2/450)*Sqrt[2*Pi]),
  {x, 55, 145},
  GridLines -> {{85, 115}, {}}
]

TRANSLATION In the code above I plot a normal curve:

1/(15*E^((x - 100)^2/450)*Sqrt[2*Pi]) 

Then tell the plot what part of the x-axis I want it to display:

{x, 55, 145}

Then I add the vertical gridlines where I want them at 85 and 115.

GridLines -> {{85, 115}, {}}

Note you need to provide the blank {} where Gridlines would expect the horizontal grid lines locations.

Solution 5

An alternative is to think of the vertical line as a straight line of infinite slope. So for a vertical line at located at x=2*pi, we can do something like this:

Plot[{Sin[x], 10^10 (x - 2 \[Pi])}, {x, 0, 10}, PlotRange -> {-1, 1}]

click to see the image

Note that the term 10^10 mimics an infinite slope. If you do not use the option PlotRange -> {-1, 1}, the "dominant" function is the straight line so the Sin[x] function do effectively appears as an horizontal line.

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Comments

[Alexey Popkov]

This recent Wolfram Blog post completely answers this question.