Question

A data set consists of the following data points:

(2,12), (3,7), (5,4)

The slope of the best fit line is -2.5. Find the y-intercept of this line.

Answer 1

We're given the slope =-2.5, and we need to find the y-intercept. y=mx+b, with "b" being the y-intercept. We have a variety of points to use, all of which result in the answer. Lets use (2,12)
\[y=mx+b \left| \right| (2,12)\rightarrow 12=(-2.5)*2+b \rightarrow 12=-5+b \ \]\[17=b\] I believe you do this with all the points and take the average to find the "best fit y-intercept".

Answer 2

What course is this for?
"Best fit" can have many definitions.
Is it the least squares fit? (Most common in statistics.)

Answer 3

It's Algebra 2

Answer 4

Well that is generally not taught at algebra 2 because in general to find it exactly quickly requires some higher math usually in algebra 2 you use a calculator to find the linear regression or you just approximate it by eye.
Here is how you can do it though with the tools of algebra 2 with just these 3 points:

Answer 5

First look at y=(-2.5)x+b for each of the 3 points.
\[(-2.5)(2)+b=12+\epsilon1\]
\[(-2.5)(3)+b=7+\epsilon2\]
\[(-2.5)(5)+b=12+\epsilon3\]
where the e terms are the "errors" the fit line minus the actual y value.

Answer 6

Then solve each so that just the e terms are on the left.

Answer 7

What's epilson?

Answer 8

You will have 3 equations each in the form of \[a+b=\epsilon\]
where a is number.
Then you square both sides of each equation.
So you will have 3 equations of the form.\[b ^{2}+c \times b+=\epsilon ^{2}\] where c and d are both numbers.
Add the 3 new equations together for an equation that looks like \[3b ^{2}+f \times b+g=(\epsilon1)^{2}+(\epsilon2)^{2}+(\epsilon3)^{2}\] where f and g are numbers.
So what we want is for these "errors" squared to be as small as possible.
So look at the left side of the equation. It is a parabola so it has a minimum value at the trough so you can find this minimum value by "completing the square" of this equation.

Answer 9

epsilon is just those e looking symbols, they are just variables.
3 different variables that are just the distance of each y of your points ( ,12) ( ,7) ( ,5) and the y that your best fit line will give.

Answer 10

Ohhh okay

Answer 11

So after all that you should arrive at \[3b ^{2}-98b+805.5=(\epsilon1)^{2}+(\epsilon2)^{2}+(\epsilon3)^{2}\]

Answer 12

This really is a complex problem for algebra 2.
I suspect that your teacher intends for you to use your graphing calculator.

Answer 13

how would you write that on a graphing calculator?