So you can represent a line using slope-intercept form and standard form but every video online that describes standard form says it's only a "different way" of representing a line. Is there really any reason to standard form or any scenario in which you would use standard form or is it just a redundant way of saying the same thing?

Is this another thread that you post and never reply to?

You mean a question? Yep! I started watching Homeland FYI :)

Thanks :P I was curious as to which advice you would take. All is forgiven!

depends on the situation and what people are used to seeing.
y=ax+b
you can rewrite as AY+BX+C = 0 if you like

It's a question of application and communication, not a mathematical one.
y=ax+b makes graphic easier
AY+BX+C = 0 makes solving systems of equations easier
by easier I mean less algebra.

*waits for Xinhuan*

To add to martian's great reply, you can also represent a straight line using vector form:

p = (a) + t(b)

where a is a point on the line, and b is a vector along the line, and t is the parametric variable. Expanding the vector math gives

(x,y) = (c,d) + t·(u,v)

so

x = c + tu
y = d + tv

which is the parametric equation of a line. The parametric form is more useful when using vector math in 2D and 3D applications.


You can also represent a line that crosses the x-axis at (a,0) and y-axis at (0,b):

x/a + y/b = 1
or
xb + ya = ab (this allows a or b to be 0)
(Note this last one is really "ay + bx + c = 0" where c = -ab)

which is really just rearranging the numbers a bit. Here, a and b are the axis-intercepts, which may be more useful than knowing the slope and y-intercept in your standard y = mx + c equation.

Oh, okay. The only answer i could come up with was that you can't represent a vertical line in slope-intercept form since x=3 for example has no y-intercept. So Martian what you're saying is that its easier to solve equations using standard form than slope-intercept form?

I just take a ruler to draw my lines straight

will there are theoretically infinite number of ways you can dream up to represent a line (ie different definitions of your vector space): such as parametric or polar or something weird (like concentric elipses) but now we are talking about linear algebra and digress from hawkeyee's question.


I was sticking to cartesian space.

@hawkeyee: no. It's easier to solve certain types of equations. if the slope of the line is of value to me (like velocity/distance problems in physics), then representing a line in that form is the most useful.
Regarding *vertical* lines: you are partly correct. Your form only allows for a subset of all possible lines. But a vertical line (infinite slope) may not make sense in some situations.

It really comes down to what makes algebra simpler for a specific set of problems. For example I can represent a line based it's point of tangency on a circle centered around (0,0) with a pre defined radius and at a specific angle from either the X or Y axis. Although this seems rather complecated, this actually is a useful representation in certain types of engineering problems (kind of).

Okay... I think I might get that.

To give the question some context which maybe I should've done at the beginning - my fiancee teaches grade 9 math and she's not sure how to answer this question in terms that a 9th grader would understand.

You use the standard form because it can represent all lines, while the slope-intercept form can't.

The slope-intercept form is however, much easier to understand visually, and it is easier to teach with.

If I told you

2Y + 3X + 5 = 0

you wouldn't be able to tell me immediately in your head how the line looks compared to y = -1.5x - 2.5

Hawkeyee: The answer she gives should depend on the student asking the question.

If it's a student with strong math/science scores, explain a good part of this thread to them.

If it's a student who has no motivation, say whatever.

Because if the student isn't paying attention, none of this discussion matters.

To help my kids get the beginning concepts of this math. We made them treasure maps in Mine Craft.

Bonus post.... :)

is this the appropriate thread for me to ask why we had to spend 2 billion dollars on a space station experiment that was designed for the sole purpose of being able to detect Wimps?

are you mad that you were the only wimp big enough to be seen from space?

no. i am a bit disappointed with your post count though. why you waste 1/4 of your posts in a failed attempt to troll me?