What linear function rule describes the graph?

Straight line equation has a general form of 
Where m is the slope 
and c is the y intercepted part.
So now, you need to find the value of the slope (m) and the y intercept (c).
As you can notice the line intercepts with y axis in (0,1) So c=1.
And then you want to find 2 points along that line  to found the slope from, we found on already (0,1) and the  other one can be any point along the line, let's take (2,3).
Then use them to find the slope.

So now m=1 and c=1.
The equation of this line is y=x+1

Hope this helps!