I am learning Machine Learning. and going through some videos. In that one slide came which I am not able to understand (Attached below). This is related to Linear Regression.
In second image, it starts line from 0's place as value of theta0 is 0. but value of theta1 is 0.5, then why he kept points at (2,1) and (1,2)?
Based on given formula, how this line is going up and how it estimates points/value.
If $h_\theta(x)=\theta_0+\theta_1 x$, and $\theta_0 = 0$ and $\theta_1 = \frac 1 2$, then simple substitution shows that $h_\theta(2) = 0 + \left(\frac 1 2\right)(2) = 1$, so $(2,1)\in h_\theta$.
(I don't think the mark at $(1, 2)$ is meant to be a point, possibly this was just the lecturer's way of drawing the viewer's attention to $h(x)$.)
To answer your question, the line is "going up" because it has a positive gradient (and has a zero intercept because $\theta_0=0$) and is used to estimate values by simple substitution.
Note that these slides are not saying anything about how good a particular model is at producing an estimate, only about how estimates are produced given the model coefficients $\theta_0$ and $\theta_1$. The next step would be to choose suitable values for $\theta_0$ and $\theta_1$ that would produce good estimates (for example, by minimising some predetermined cost function based on the parameters and the points that are supposed to be modelled).