Question

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

Answer 1

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

Answer 2

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

Answer 3

equations*

Answer 4

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.

Answer 5

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

Answer 6

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.

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

where N is the number of experimental points

Answer 12

experimental points? what does the E stands for?

Answer 13

where is the E ?

Answer 14

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

Answer 15

The big numberal sign you see repeating

Answer 16

'∑' this sign ?

Answer 17

Oooh it stands for equation

Answer 18

it is the capital \sigma

Answer 19

\[\Large \Sigma \] stands for summation

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

Im not sure anybody told me yet :-:

Answer 24

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

Answer 25

oh ok .. O_o

Answer 26

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

Answer 27

I remember hearing about rise over run

Answer 28

but what does the numbers do ?

Answer 29

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

Answer 30

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

Answer 31

Oh so they are just for show?

Answer 32

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

Answer 33

Oh ok

Answer 34

You pronounce "y2" as "y sub 2"

Answer 35

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

Answer 36

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

Answer 37

Oh ok I think Im good thanks

Answer 38

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.