What is the equation of this line of best fit in slope-intercept form?

- anonymous

What is the equation of this line of best fit in slope-intercept form?

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- anonymous

Dan drew the line of best fit on the scatter plot shown below:

##### 1 Attachment

- Michele_Laino

here we have to apply the least square method, in order to get the right equation for constants A and B, such that:
y=Ax+B

- Michele_Laino

equations*

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- anonymous

Since you already have the line of best fit you first need to understand the concept of slope-intercept form which is: y = mx + b
I'd first calculate the y-intercept then slope.

- anonymous

so then Its either y = 3x + 5/6 or y = 3x + 6/5

- anonymous

You're mixing the y-intercept and slope up…
the y-intercept is the point of the line where x = 0. That would make (0, 3) the y-intercept.

- anonymous

As for the slope, try again.. you understand the basic concept.

- anonymous

The y-intercept is where the point and line meets?

- Michele_Laino

here are the formulas for the coefficients A, and B:
\[\Large \left\{ \begin{gathered}
A = \frac{{N\sum {{x_i}{y_i} - \left( {\sum {{x_i}} } \right)\left( {\sum {{y_i}} } \right)} }}{{N\sum {x_i^2 - {{\left( {\sum {{x_i}} } \right)}^2}} }} \hfill \\
\hfill \\
\hfill \\
B = \frac{{\left( {\sum {x_i^2} } \right)\left( {\sum {{y_i}} } \right) - \left( {\sum {{x_i}} } \right)\sum {{x_i}{y_i}} }}{{N\sum {x_i^2 - {{\left( {\sum {{x_i}} } \right)}^2}} }} \hfill \\
\end{gathered} \right.\]

- anonymous

The y-intercept is where the line crosses the y-axis.

- Michele_Laino

where N is the number of experimental points

- anonymous

experimental points? what does the E stands for?

- Michele_Laino

where is the E ?

- Michele_Laino

with experimental points, i mean the number of points, namely:
N=11

- anonymous

The big numberal sign you see repeating

- anonymous

'∑' this sign ?

- anonymous

Oooh it stands for equation

- Michele_Laino

it is the capital \sigma

- Michele_Laino

\[\Large \Sigma \] stands for summation

- anonymous

Im not getting how to find the slope intercept..?

- Michele_Laino

for example, we have:
\[\Large \sum\limits_{i = 1}^5 {{x_i}} = {x_1} + {x_2} + {x_3} + {x_4} + {x_5}\]

- anonymous

O_O what does all those signs and numbers suppose to mean again?

- anonymous

Im not sure anybody told me yet :-:

- Michele_Laino

nevertheless I think that we have to write the equation of the line represented in your drawing. In order to that we note that your line passes at point (5,9) and at point (10,15)
so we have to write the equation of a line which passes at those points

- anonymous

oh ok .. O_o

- anonymous

In order to calculate slope, note that it is rise/run or:
y2 - y1/x2 - x1
(Using two points to plug in)

- anonymous

I remember hearing about rise over run

- anonymous

but what does the numbers do ?

- anonymous

Awesome!
The numbers next to the x and y are sub numbers… they don't really mean anything

- anonymous

I mainly used to refer to them as numbers that would help me keep organized

- anonymous

Oh so they are just for show?

- anonymous

Technically, no, but you can look at it that way :)

- anonymous

Oh ok

- anonymous

You pronounce "y2" as "y sub 2"

- anonymous

if i had a equation like this : y = 3x + 6/5 why is there a fraction in their and what do i do about it

- anonymous

Well, "6/5" represents slope: meaning that you would rise 6 units, and run (towards the right since it is positive) 5 units.

- anonymous

Oh ok I think Im good thanks

- anonymous

Okay, cool!
So, usually I start at the y-intercept before I rise or run if I have a graph.. there are many ways to calculate slope, but since you have a graph, it's easier to have a visual representation that way.

- anonymous

|dw:1436729744129:dw|

- anonymous

So, we can choose ANY two points that are on the line.

- anonymous

Let's take:
(1, 4)
(5, 9)

- anonymous

We can name both of these pairs as:
(x1, y1)
(x2, y2)
Make sense?

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