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Discuss the slope, $y$-intercept and graphs of the following:

  a) $y=5$
  b) $x=-3$

How can I answer this in discussion form?

2 Answers 2

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"Discuss the slope" just means "talk about the slope". The reason the question is phrased that way is because, while a horizontal line has a slope, a vertical line does not. Hence, you can say something like "the slope of a vertical line is undefined", or something to that effect.

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There is a mnemonic device: HOYVUX
H orizontal lines have
0 (zero) slope and their equations are
Y = (some constant)

V ertical lines have
U nderfined slope and their equations are in the form
X = (some constant)

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    Also, a vertical line $x = c$ has no y-intercept, and x-intercept (c, 0). Likewise, a horizontal line $y = c$ has no x-intercept and the y-intercept is (0, c)2011-09-30
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    Unless, of course, $c = 0$.2011-09-30
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    WLOG assume $c \neq 0,\pm \infty$2011-09-30
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    You do lose generality by assuming $c \ne 0$, since $c = 0$ is a qualitatively different case. You might argue that it's trivial, but then, so is $c \ne 0$ too.2011-10-01
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    I might argue that your sense of humor is qualitatively different than mine... Without loss of generality, of course.2011-10-01