Graphing vertical lines

[Kira]

I was wondering if there is a way to graph vertical lines on the
nspire. The Inequalz program for the 84 allowed you to switch to an
"x=" screen where you could type in the equation and the calculator
would then graph them. I haven't been able to come up with a solution
(typing in x doesn't work), and I was hoping someone out there had a
way to do this! We are graphing systems of inequalities and it would
be nice to be able to graph vertical lines!

Thanks!

Kira Christensen
Washington High School
Sioux Falls, SD

[Sean Bird]

How about this for an option...
MENU, 9:Construction, 1:Perpendicular

Draw lines perpendicular to the x axis. Use MENU, Action, Coordinate & Eq if you want to know the equation of that line (it will say x= ___). Similarly reveal the coordinates of the point on the x axis and you can move this line by changing the value for x.

Sean Bird
Indianapolis, IN

--
Sean Bird
AP Calculus & Physics,
NHS Adviser & Rocket Team Supervisor
Math & Science Technology Coordinator
Covenant Christian High School
7525 West 21st Street
Indianapolis, IN 46214
Phone: 317/390.0202 x104 Fax: 317/390.6823
Website: http://covenantchristian.org/bird
work Email: sean...@covenantchristian.org
personal Email: covena...@gmail.com
Psalm 111:2 "Great are the works of the LORD, studied by all who delight in them."

[Chris Martin]

I have attached a very simple problem that allows you to enter in multiple
linear combinations of a system and it graphs each line. The vertical line
will appear automatically based on the intersection of the system. In the
example, I used 3x+4y=7 and 2x-2y=6 as the original system and then enter
some other combinations of those two equations.

--
Chris Martin
Marion High School
chma...@marion.k12.ia.us

[Eagle-Man]

Another method, as described in the latest TI Nspiring Times (Nspire
newsletter/magazine, pg. 12), is to use Menu, 6:Points & Lines, 4: Line.

With this you can create a line using two points. The first point
(P1) is the anchor of the line and is the centre of rotation. If you
grab the line, you can rotate it until it's vertical, and also grab P1
to move it horizontally.

Then you can use Menu, 1:Actions, 7:Coords & Equations, click on the
line to show the equation. It should be of the form x=k.

As stated in the Times, "The 'geometry' of this line is much different
than the 'geometry' of the graphed line that is typed into f1(x).
Since this line was created using two points, it can be rotated and
moved in a different manner."

[John Mahoney]

I've been creating vertical lines on Graph and Geometry pages by using
parametric functions. For example, setting x1(t) = 3 and y1(t) = t
will graph the vertical line x = 3. In my work, I set x1(t) = p
where p is a parameter controlled by a slider. In that way, the user
can move the vertical line left or right as necessary.

John F. Mahoney
Benjamin Banneker HS
Washington, DC

> > work Email: seanb...@covenantchristian.org
> > personal Email: covenantb...@gmail.com

> > Psalm 111:2 "Great are the works of the LORD, studied by all who delight in

> > them."- Hide quoted text -
>
> - Show quoted text -

[Kira]

Thank you for all the responses! I'm still looking for a way to graph
vertical inequalities, however. I think that I need to be able to
create the vertical inequality in the graphing function of the
application as opposed to the geometry portion so that it will shade
the appropriate side of the graph. For example graphing the system:
y>-2, y<x-4, and x<4. I'd like to be able to show students where the
shading of the graphs overlap, but I haven't been able to include the
vertical line's shading. Any ideas? Thanks again!

Kira Christensen
Washington High School
Sioux Falls, SD

> > - Show quoted text -- Hide quoted text -

[Sean Bird]

Here is a creative idea. I don't know if my explanation will be sufficient to implement, but if you
1. make the vertical line using a method discussed below (like perpendicular line)
2. Show the coordinates of the point used to create the vertical line. Store the x-value (You can use that value and make a slider using that same variable)
3. Using Shape, Polygon make a big square with two of the points on the the vertical line.
4. Use attributes to shade the square.
5. Change the window so you cannot see the edge of the square.
There you have it.
You could make the other end of the square another line with the x-coordinate stored as a variable. If you wanted to change the x>= to <= you could change that value (perhaps in a spreadsheet) so that it is far on the other side. Also in attributes you could change the line to dotted or dashed so it looks proper for x>2, for example.

Sean Bird
Covenant Christian HS
Indianapolis

On Fri, Oct 10, 2008 at 10:54 AM, Kira <kir...@gmail.com> wrote:

Thank you for all the responses! I'm still looking for a way to graph
vertical inequalities, however. I think that I need to be able to
create the vertical inequality in the graphing function of the
application as opposed to the geometry portion so that it will shade
the appropriate side of the graph. For example graphing the system:
y>-2, y<x-4, and x<4. I'd like to be able to show students where the
shading of the graphs overlap, but I haven't been able to include the
vertical line's shading. Any ideas? Thanks again!

Kira Christensen
Washington High School
Sioux Falls, SD

This topic reminded me to share a tip that some of you geometers may particularly like.
I notice that if you have

[Rex Boggs]

Some very clever ideas here.

 

However it would be better if the TI-Nspire had the option to just graph x = a and the associated inequalities (and do the correct shading).  Can TI please consider this for a future OS upgrade?

 

BTW, when we teach Linear Programming, we always shade the areas that are NOT in the feasible region.  The feasible region then is the area that is unshaded.  It is much easier to see.

 

Cheers

 

Rex

 

[Pat Flynn]

I noticed that about you Australian's and Brit's. The Autograph
program I use has that setting as a default and it is from England.

[Sean Bird]

I agree that it could be a lovely feature to add, however at the same time I like the response my TI-Nspire CAS gives me when I, like Kira mentioned, backspace from "f(x)=" and enter x=2, for example. It says "Not a function."

Actually, if you type "x=" it tries to change it to "x(x)="
Note: When an inequality replaces the equals sign, the f1(x) changes to y.

I had recently thought about using the response "Not a function" as a pedagogical tool in the introduction of the definition of function. But if we are hoping they'll add that, then I ought not make that part of an activity that might be posted on the activity exchange.

Have a great weekend.

Sean

[Eagle-Man]

It is my understanding that graphing an inequality with a vertical
line is impossible on the Nspire. The inequalities are graphed using
the Function part of the application, and, as the vertical line is not
a function, it cannot be done.

I doubt that TI would add this functionality into the application
because then it would open the door for any x= graph, as well as
trying to enter any other letter (ie: g=), and would require a near
complete rewrite of the entire application.

Also, the way that TI has designed this application is that we can
enter the graphs in functional notation (ie: f(x)=), and adding the x=
functionality might cause some conflict between parsing the two
notations, and I think that the functional notation would be more
useful and more important.

Finally, I'd just like to (re)state that the way that TI has
implemented this app returns "Not a Function" when x= is entered as a
graph. As Sean pointed out, this could be used as a teachable moment,
possibly asking the students why it (and other similar graphs) is not
a function. If TI changed the app to accept x= notation, then there
would NOT be any such case where "Not a Function" would be given - it
would be able to graph pretty much anything.

I for one like it the way it is.

[Landy Godbold]

I have long used the "shade the other side" for Linear Programming
settings for just the reason Rex suggests. The way I get around
vertical boundaries is to use point-slope form (use the x-intercept as
your point) and graph a line with a very large slope, but not really
vertical. It will LOOK vertical, and you can shade it easily.

cheers,
landy

[Bryson Perry]

I think it would be nice if their was an option of Graph Type: Implicit  so that the TI-Nspire could graph a circle of the form x^2 + y^2 = 25 or x=? While in this graphing option the calculator might be able to graph things that are not functions, but the teachable moment is still available when in Function graphing.

Bryson

---

> Date: Sat, 11 Oct 2008 12:47:39 -0400
> From: l.go...@comap.com
> To: tins...@googlegroups.com
> Subject: [tinspire] Re: Graphing vertical lines

[Tracy]

I think Bryson has found the best of both worlds here! Now we could
look at standard forms of ellipses and hyperbolas too AND keep Sean's
teachable moment. Bravo!

Tracy

On Oct 11, 6:51 pm, Bryson Perry <brysonperr...@msn.com> wrote:
> I think it would be nice if their was an option of Graph Type: Implicit  so that the TI-Nspire could graph a circle of the form x^2 + y^2 = 25 or x=? While in this graphing option the calculator might be able to graph things that are not functions, but the teachable moment is still available when in Function graphing.
> Bryson
>

> > Date: Sat, 11 Oct 2008 12:47:39 -0400> From: l.godb...@comap.com> To: tins...@googlegroups.com> Subject: [tinspire] Re: Graphing vertical lines> > > I have long used the "shade the other side" for Linear Programming > settings for just the reason Rex suggests. The way I get around > vertical boundaries is to use point-slope form (use the x-intercept as > your point) and graph a line with a very large slope, but not really > vertical. It will LOOK vertical, and you can shade it easily.> > cheers,> landy> > > > > > Pat Flynn wrote:> > I noticed that about you Australian's and Brit's. The Autograph> > program I use has that setting as a default and it is from England.> > > > On Oct 10, 3:53 pm, "Rex Boggs" <rexbog...@optusnet.com.au> wrote:> > > >>Some very clever ideas here.> >>> >>However it would be better if the TI-Nspire had the option to just graph x = a and the associated inequalities (and do the correct shading). Can TI please consider this for a future OS upgrade?> >>> >>BTW, when we teach Linear Programming, we always shade the areas that are NOT in the feasible region. The feasible region then is the area that is unshaded. It is much easier to see.> >>> >>Cheers> >>> >>Rex> > > > > > > > > > > > > > _________________________________________________________________
>
> Want to do more with Windows Live? Learn “10 hidden secrets” from Jamie.http://windowslive.com/connect/post/jamiethomson.spaces.live.com-Blog...

[Sean Bird]

I don't know what code the TI-Nspire uses to graph, but it definitely looks different than the 84 or 89.
It almost seems like Graph Type: Implicit wouldn't be too difficult to add. Having it as a built in feature would likely be more powerful than the implicit program I've used (see http://www.johnhanna.us/TI-nspire.htm).

Where would "x<2" fit in? I think I have graphed implicit inequalities with GrafEq software in the past. Hmm, I looked it up again, implicit equation graphs sure can get ridiculously complicated; e.g. http://www.peda.com/grafeq/gallery/frontispiece.html 

I have enjoyed using the TI-Nspire to draw a circle (MENU: Shapes) and then asking the Nspire to give the equation (Action: Coordinates and Equations). An example of the result is (x+6)^2 + (y-2.5)^2 = (3.3)^2.
HEY, put a tangent line on your circle. Have its equations shown. Drag it around the circle and see "x= something" appear when the tangent line is vertical. Nice!

Sean Bird
Indianapolis, IN

[Eagle-Man]

The code for the Nspire would definitely need to be different from
anything previous because of a) the cursor, b) dynamic manipulation of
the axes, c) direct manipulation of the function, d) dynamic update of
the equation, etc.

What you suggest is a good idea, but again, it would probably require
too much reworking of the code. Remember, it's not just about
graphing the equation, but about maintaining the complete
functionality of manipulation at the same time.

It would probably have to be the case that while in function mode, it
could not draw non-functions, and while in non-function mode, could
not draw functions, so there would have to be a constant check for
what mode you're in.

OR, if the implicit mode could also draw functions, then there would
be a lot of redundant code.

Personally, if I was programming this, I would leave it as it is,
because things like circles and vertical lines ARE possible to do
fairly easily (and you can get/change the equations), and it would be
too much work to change.