How to Graph a Linear Function

[matheus]

Hey guys,

In the image below, I understand that the equation is a linear function, but I am unsure how to graph it and present it in the way requested

For those who cannot see tinypic images:

[box=green]Draw the graph of $s=1400(t-15)+150\,000$

Put $s$ on the vertical axis and cover the time interval $15\le t\le35$[/box]

Can anyone help me out?

Thank you so much :)

 

[MarkFL]

I would plot the two points:

$$(15,s(15)),\,(35,s(35))$$

and then connect the two points to create a line segment with the two points as terminals. Can you proceed?

 

[matheus]

Hi MarkFL,

Thank you for the reply :-)

Ah I see, is that similar to plotting coordinates then? I'm still a bit unsure of how to plot them, but I understand the concept :-/

Also I would like to draw the graph using a graphing calculator online, does that make things a bit trickier?

Thank you so much for your help :-)

 

[Jameson]

The variable names might be a bit confusing. This is really the same as graphing $y=1400(x-15)+150\,000$. Instead of graphing this for all $x$ though, we are only graphing it from $15\le x\le35$. Just want to point this out if it wasn't already clear. :)

We have a wonderful graphing calculator tool from Desmos that works in posts here. For example, if you want to graph $y=x^2$ you can do that. Click on the green button next to the $$\Sigma$$ in the toolbar to use it.

[desmos="-10,10,-10,10"]y=x^2[/desmos]

To answer your question about Mark's post - What is the y-coordinate for $t=15$? What about $t=35$?

 

[MarkFL]

Yes, you can let $t$ be any value (it is the independent variable), and then using the value of $t$, you can compute the corresponding $s$ coordinate using the given function definition. Since you are told to let $15\le t\le35$, I recommended using the two boundaries for $t$ as the end-points of the resulting line-segment.

So, for example, if $t=15$, then $s(15)=1400(15-15)+150000=150000$, so we know $(15,150000)$ is the left end-point. Can you find the other end-point?

As far as using an online graphing tool, we offer a Desmos Graphing Calculator API button on our toolbar:

[desmos="15,35,150000,178000"]s=1400(t-15)+150000;15\le t\le35[/desmos]

edit: I see Jameson and I are thinking the same thing...:D

 

[matheus]

Hi Jameson and MarkFL,

Once again thank you very much for your help here, greatly appreciated! :D

The Desmos graphing tool is excellent and is just what I'm looking for (Yes)

So, for example, if t=15, then s(15)=1400(15−15)+150000=150000, so we know (15,150000) is the left end-point. Can you find the other end-point?

Ok so if the left end point is (15,150000), then I think I have calculated the right end point to be:

When t=35, s=178 000, the second set of coordinates would be (35,178000), am I getting closer?

 

[MarkFL]

Hi Jameson and MarkFL,

Once again thank you very much for your help here, greatly appreciated! :D

The Desmos graphing tool is excellent and is just what I'm looking for (Yes)
Ok so if the left end point is (15,150000), then I think I have calculated the right end point to be:

When t=35, s=178 000, the second set of coordinates would be (35,178000), am I getting closer?

Yes, you have correctly calculated the right end-point, so now just plot the two points (on an appropriately scaled coordinate system) and connect them with a line segment. :D

I would likely let the $s$ axis have units of $10000$, and then you can effectively plot $(15,15),\,(35,17.8)$.

 

[matheus]

Hi MarkFL,

Great! :D

Ok so the last thing I need to work out now is how to show that using the Desmos graphing tool. Now I know how to plot two points on a piece of graph paper, but I haven't quite figured out how to do it on there (haven't had my coffee yet so I'm not fully alert, lol)..

Sorry to be so dumb, but is there a way to just enter the coordinates into that software?

 

[MarkFL]

Yes, you can get Desmos to plot points, for example the code:

[desmos="10,40,0,200000"]s=1400(t-15)+150000;15\le t\le35;(15,150000),(35,178000)[/desmos]

will produce:

[desmos="10,40,0,200000"]s=1400(t-15)+150000;15\le t\le35;(15,150000),(35,178000)[/desmos]

 

[matheus]

Hi MarkFL,

That is genius, thank you so much! :D

I will have a play around with this Desmos tool, it's excellent isn't it (Yes)

Before I read your reply, I had a quick test of another graphing tool and got the following result:

Not as neat as Desmos but still useful

 

[MarkFL]

...Not as neat as Desmos but still useful

What really sets the Desmos API apart from other apps, is that the graphs you embed in your posts can be interacted with, unlike a static image taken from a screenshot and posted. You can add functions and sliders, zoom in and out, drag the graph, just to name a few actions.

As far as I know, you won't find this API on any other math help site either. (Muscle)

 

[matheus]

Yeah it is really impressive stuff, and so nice to use as well (Yes)

Thank you guys once again for your help with my question, I really do appreciate you taking the time to explain things so clearly :D

Have a great day! (Yes)