Answer
The function is
$$f(x)=2x+1.$$
The graph is on the figure below
Work Step by Step
The equation of the linear function passing through points $P(x_1,y_1)$ and $Q(x_2,y_2)$ is given by
$$y=\frac{y_2-y_1}{x_2-x_1}(x-x_1)+y_1.$$
Using the data given in the problem
$$x_1=1\quad y_1=3,\quad x_2=2,\quad y_2=5$$
we get
$$y=\frac{5-3}{2-1}(x-1)+3=2x-2+3=2x+1$$
so our linear function is
$$f(x)=2x+1.$$
Drawing the line through points $(1,3)$ and $(2,5)$ we get the required graph
