In general, given two distinct points there is one line which passes exactly through both. If the points are \((x_1,y_1), (x_2,y_2)\) then presuming the x-values are different gives the equation
\begin{equation*}
y = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1) + y_1
\end{equation*}
is the linear function which passes through both points. If the x’s are equal then
\begin{equation*}
x = x_1
\end{equation*}
is your linear equation. However, once you collect three or more points it is likely that there is no line which exactly "interpolates" all of the points. So, to accommodate this increased complexity, the complexity of the model also must increase. For example, a quadratic might be a good model to fit three points or a 6th degree polynomial might be a good model to fit seven points. However as the number of points increases significantly, the use of a model that exactly interpolates at each of the data points becomes problematic due to its complexity and the trouble expended in order to obtain the model.