It does represent a direct variation.
Direct variation: y = kx
y varies directly with x
Your equation 2y = 5x + 1 is in the form of y = kx but we need to divide out the 2 from 2y so we have the following
2y = 5x + 1
2y / 2 = 5 x/ 2 + 1/2
y = 5x / 2 + 1/2
y = kx
k = 5/2
k = constant of variation = 5/2
so maybe 6 plus 3 which equals 9. Then add 8 at the end
LHS: =

(using

)
We know

so we can replace the sin²x in the LHS expression as follows

which is the RHS.
5 days food for 150 students suggests there was 750 day rations
If there was 100 students this would last 750/100 = 7.5 days.
If it ran out after 4 days there were 750/4 = 187 students (187.5 not valid)