Homework Help: Straight Line Graphs -Plotting, Gradient, Intercept & Finding Equation

1. Dec 5, 2011

lloydowen

1. The problem statement, all variables and given/known data
I have an issue with Straight Line graphs, I have never done them before (I touched on them in Seconday School, y=mx+c that sort of stuff) Now I've been faced with a problem that I need to learn. It's not homework it's revision but I thought it was more relevant to post here :P

Questions
a) Plot the Graph R vs T (R Vertical, T Horizontal)
b) Find the gradient and intercept
c)Establish the equation of the graph
d) Calculate R when t = 200

2. Relevant equations

3. The attempt at a solution

I don't have graph paper available :( But...

Any help/guidance at all would be appreciated, I realise the size of the question :)

2. Dec 5, 2011

eumyang

It looks like you'll need to draw a best-fitting line for the scatter plot. Check this link to see how. Once you draw the line, pick two points on the line (they don't necessarily have to be the data points), and use them to find your slope and y-intercept.

3. Dec 5, 2011

lloydowen

Thanks buddy! I'll give it a go now :)

4. Dec 5, 2011

lloydowen

Ok, so I picked two points, but what do I do with them? I looked at that link and it doesn't show what to do next :/

5. Dec 5, 2011

eumyang

If you have two points
(x1, y1) and (x2, y2)
you find the slope using this formula:
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

Then you take the slope-intercept form the equation,
y = mx + b,
and plug in the slope you just found for m, and one of the points for x and y (doesn't matter which one), and solve for b, the y-intercept.

6. Dec 5, 2011

lloydowen

Alright, so I worked out that my M=0.4
So $y=(0.4)(47) + (b)$ What is B? That website that b=(y)intercept That's a little confusing because I thought we were trying to find (y) ?

7. Dec 5, 2011

eumyang

No, we want to find b, the y-intercept, first. To do so, you'll also need to plug in the y-coordinate of the point you used (was it 120?):
$120=(0.4)(47) + b$

8. Dec 5, 2011

lloydowen

It was 118, so then do I need to re-arrange that formula then to get b the subject?

9. Dec 5, 2011

lloydowen

Actually sorry yes It was 120, I read the wrong column..

10. Dec 5, 2011

eumyang

Yes, you have to solve for b.

I noticed that the variables used are t and R. You'll have to change to equation to
R = 0.4t + b,
after you find b.

11. Dec 5, 2011

lloydowen

So if $(0.4)(47)= 18.8$ then would it be $b=120-18.8$

12. Dec 5, 2011

eumyang

Yes, although I'm wondering about your slope, m. Is it exactly 0.4? If not, use the "exact" value instead for your slope.

13. Dec 5, 2011

lloydowen

Well it wasn't because of the type of paper I was using, but I use a graph on the computer and it came to 0.43.

So then if $120=(0.43)(47) + b$ Correct me if im wrong but $b=120-20.21$? So would 'b' be (sounded confusing lol) 99.

14. Dec 5, 2011

lloydowen

Not sure what happened there [tex]b=99.79[/itex]?

15. Dec 5, 2011

eumyang

b = 99.79 sounds reasonable. Now you have
R = 0.43t + 99.79.
Now do part (d).

16. Dec 5, 2011

lloydowen

So... $T=200, R=200(0.43)+99.79 = R= 185.79$

17. Dec 5, 2011

lloydowen

Thanks so much! I really do owe this forum a lot, and after this exam I will be answering questions that people have on here (if I can) :D:D:D Such a great community here!