Straight Line Graphs -Plotting, Gradient, Intercept & Finding Equation

[lloydowen]

Homework Statement

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

Homework Equations

The Attempt at a Solution

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

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

 

[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.

 

[lloydowen]

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

 

[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 :/

 

[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.

 

[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) ?

 

[eumyang]

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) ?

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?):
$120=(0.4)(47) + b$

 

[lloydowen]

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

 

[lloydowen]

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

 

[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.

 

[lloydowen]

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

 

[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.

 

[lloydowen]

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

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 I am wrong but $b=120-20.21$? So would 'b' be (sounded confusing lol) 99.

 

[lloydowen]

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

 

[eumyang]

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

 

[lloydowen]

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

 

[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!