If the points lie on a line then there will be constant gradient or slope. Let's see.
Call the points A, B, C and D in order. The slope between A and B=(8-4)/(3-0)=4/3.
The slope between B and C=(28/3-8)/(4-3)=(28-24)/3*1=4/3.
The slope between C and D=(32/3-28/3)/(5-4)=4/3.
The function is f(x)=4x/3+b, where b is the intercept we have to find. To do so substitute the values for one point. Let's pick A: f(0)=4=b, so f(x)=4x/3+4. You should find all the points fit the function. (And they do!)