Easiest way to make a graph is to make a table of values. This gives a set of inputs (x-coordinate) and outputs (y-coordinate), which we will use to graph.
f(t) = 1.5t + 5
For instance, when t = 0, the output, f(t) = 5. When t = 1, f(t) = 6.5, f(2) = 8, and so on.
A shortcut to this is using the slope to our advantage. We can see that as t increases, f(t) increases by 1.5. Using this logic, going backwards would subtract 1.5 from the output.
f(-1) = 3.5, f(-2) = 2, etc.
Hope this helps.