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There is sudden (sharp, this means, it's not differentiable at that point) change in the gradient of a line:

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What is the proper way to refer to it, to not sound too mathematical. For example, "this line has a kink in it" seems odd. "The line has a break in it" might mean that there is a gap.

Edit: what I would like to finally express is how one adds this property to the line. E.g: "With this method, you can add a [noun] to the line", or "you can [verb] the line."

I don't need to emphasize the abruptness (but don't want it to be misunderstood as making a curve out of it). I would just like to make it clear, in simple terms, what would happen to the line.

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Why not simply a bend in the line? –  bib Nov 22 '13 at 13:02
    
@bib: Wouldn't that imply that the line becomes curved? –  vsz Nov 23 '13 at 15:44
    
This [definition]9http://www.collinsdictionary.com/dictionary/american/bend?showCooki‌​ePolicy=true) says curved or crooked form. You could say sharp bend which most people would probably read as an angle between two straight sections. –  bib Nov 23 '13 at 18:21
    
You call it "Kanye West's musical consistency between 2004 and present." –  Mr_Spock Nov 27 '13 at 12:46
    
Corner ... "See, Mary, the corner in the graph occurred when the first iPhone was announced." –  GEdgar Nov 27 '13 at 13:24

4 Answers 4

How about:

the line changes in steepness.

You can add more detail too, if you need to describe the level of change.

the line severely changes in steepness.

the line slightly changes in steepness.

Following discussion and your edits, I would suggest.

With this method you can add an angle to the line.

Or, if you're happy to use multiple words, you will be much clearer saying:

With this method you can add a change of direction to the line.

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What I would like to express is how one can "add" such a change. If I wrote "you can add a change in its steepness" it might mean that "you can change its steepness (for the whole line)" –  vsz Nov 22 '13 at 10:51
    
"You can alter the direction/steepness of the line"? –  Ste Nov 22 '13 at 10:52
    
That would mean that I alter the steepness of the whole line. What I mean that the line had uniform steepness, and I added the change, and it no longer has that uniform steepness. –  vsz Nov 22 '13 at 10:59
    
So you want to be able to say: "I added a [noun] so the line changed in steepness"? –  Ste Nov 22 '13 at 11:01
    
No, "I added a [noun] to the line." Without further explanation. "The line changed in steepness" might still imply that the whole line changed. –  vsz Nov 22 '13 at 11:07

skew

noun 1 an oblique angle; a slant.
verb 1 [no object, with adverbial] suddenly change direction or position: the car had skewed across the track

OP's use case, with skew:

With this method, you can add a skew to the line.

Though I would suggest using a verb form instead:

With this method, you can make the line to skew (at a given point).

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We normally use the word abrupt.

  • Abruptness, for a descriptive noun.
  • Abrupt change.
  • Acute change.

Frequently, people use sudden and abrupt interchangeably. However, there is a significant difference between sudden and abrupt.

Sudden should be restricted to abruptness in the time dimension. Whereas, abrupt is applicable to any "sudden" change in any dimension.

However, it is risky to use acute when trying to describe a mathematical chart or phenomenon in lay terms, because there is confusion between its meanings mathematically (in geometry) and colloquially.

"Please be careful, there is an abrupt change in the speed limit from 70 mph to 35 mph at that stretch of the road. After which, there will be an abrupt bend." The instructor said suddenly.

We were surprised when we noticed the abrupt change in the curve. The rate of increase in pressure abruptly decreased with the increase in temperature.

From American Heritage Dictionary ...

a·brupt adj.
1. Unexpectedly sudden: an abrupt change in the weather.
2. Surprisingly curt; brusque: an abrupt answer made in anger.
3. Touching on one subject after another with sudden transitions: abrupt prose.
4. Steeply inclined. See Synonyms at steep1.
5. Botany Terminating suddenly rather than gradually; truncate: an abrupt leaf.

Compare with ...

sud·den
adj.
1. Happening without warning; unforeseen: a sudden storm.
2. Characterized by hastiness; abrupt or rash: a sudden decision. See Synonyms at impetuous.
3. Characterized by rapidity; quick and swift.
Idiom:
all of a sudden
Very quickly and unexpectedly; suddenly.

a·cute
adj.
1. Having a sharp point or tip.
2. Keenly perceptive or discerning: "a raw, chilling and psychologically acute novel of human passions reduced to their deadliest essence" (Literary Guild Magazine). See Synonyms at sharp.
3. Reacting readily to stimuli or impressions; sensitive: His hearing was unusually acute.
4. Of great importance or consequence; crucial: an acute lack of research funds.
5. Extremely sharp or severe; intense: acute pain; acute relief.
6. Medicine
a. Having a rapid onset and following a short but severe course: acute disease.
b. Afflicted by a disease exhibiting a rapid onset followed by a short, severe course: acute patients.
7. Music High in pitch; shrill.
8. Geometry Having an acute angle: an acute triangle.

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The line is angled or broken.

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It is a sharp change, I edited the question. So you might recommend "You can add an angle to the line"? –  vsz Nov 22 '13 at 11:05
    
"With this method you can break the line at an angle" / "With this method you can add a break at an angle to the line" ? Probably the first. –  vsz Nov 22 '13 at 11:12
    
@vsz: Yes, the first is best. –  SF. Nov 22 '13 at 11:15
    
Broken by itself is appropriate; I've never seen broken used to mean a discontinuity, and would regard such usage, if it actually ever did occur, as a mistake. “Broken at an angle” is an odious pleonasm. Both of the line segments in the questions example are angled (in the sense of being neither vertical nor horizontal). -1, but will cheerfully refund the downvote if you fix all those issues –  jwpat7 Nov 22 '13 at 17:37
    
@jwpat7, ‘broken line’ does indeed very often refer to a line that is discontinuous—in fact, if you look it up in various dictionaries, you will see that a broken line is most commonly defined as something like, “a discontinuous line or series of line segments, as a series of dashes, or a figure made up of line segments meeting at oblique angles”. It is by no stretch of the imagination a mistake to call a discontinuous line broken. The line in the middle of roads and streets is often called a ‘broken white line’. –  Janus Bahs Jacquet Nov 23 '13 at 14:34

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