It is a linear function because of the equal differences in the x-y values. So we can write the function as y=mx+a where a and m are constants. When x=0, y=3 so a=3. To find m we take any pair of points to work out the slope, so let’s use the first pair: m=(3-1)/(0-(-1))=2, therefore y=2x+3.
Check by putting in a value for x from one of the points we haven’t used yet. Pick x=2, which makes y=2×2+3=7, which gives us the point (2,7) one of the listed points.