How do I know what the slope of the line is by being provided Theta(1) (aka ø(1)) ? (Cost function and linear regression)

Question

Andrew Ng is explaining linear regression and the cost function, and why we want to minimize Theta(1).

However, he says that when Theta(1) = 1 then our slope of the line is (x,y) = (1,1), (2,2), (3,3).

I don't understand how he computes that slope? I don't understand how to figure this out? How do you know that the slope of the line is that?

http://cl.ly/image/1J1n2E151k2n

For example, what happens when Theta(1) = 2, how would i figure out the slope?

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For more detail, you can see: https://class.coursera.org/ml-2012-002/lecture/index, at 2:30 he mentions that if Theta(1) = 1, then the slope of the line is: (1,1), (2,2), (3,3), or http://cl.ly/image/1J1n2E151k2n

Answer 1

It is not θ$_1$ that is minimized , it is the sum of squared errors that is minimized. Ng is fitting an equation either of the form Y=θ$_1$X. Note that the other link does not connect properly. When θ$_1$=1 the line is Y=X. θ$_1$ is the slope and that is why it goes through the points (1,1) (2,2) etc. Now if the slope θ$_1$=2 then the line would go through the points (1,2) (2,4) (3,6) etc.

Answer 2

I just learned that in this example, ø(0) is the y-intercept and that ø(1) is the slope of the line.

Thus if ø(1) = 2, then the coordinates will be (1,2), (2,4), (3,6)