We are asked to determine what expression represents a line with slope 1/3 and passing through the point (-2,1)
A slope of 1/3 means that for every three units displaced horizontally, there is a displacement of 1 unit vertically
If we detail the possible expressions they all meet the 1/3 slope, but they have an added number that generates a displacement of the whole function
For this let's remember the translations of a function, where it says that if we have the expression f(x+c) being c a number, this is translated horizontally "c" units to the left
If we want the line to pass through the point (-2,1) and we know that for three horizontal units we move one vertical unit, the line must pass through (-5,0) for that we add 5/3
Since the slope is 1/3 the denominator does not affect us and instead, the numerator moves the line 5 units to the left
In conclusion, the answer is:
[tex]y=\frac{1}{3}x+\frac{5}{3}[/tex]
