In Beloy's fish ball factory, it costs 25 pesos to make 15 pieces of fishball while it costs 40 pesos to make 27 pieces. Assuming that the total cost is described by a linear function, how much does it cost to make 19 pieces of fishball?

You are given 2 ordered pairs of the form

(fishballs, cost), they are (15,25) and (27,40)

just follow the same steps you would when finding any linear function
slope = (40-25)/(27-15) = 15/12 = 5/4

cost - 25 = (5/4)(fishballs - 15)
cost = (5/4)fishballs - 75/4 + 25
cost = (5/4)fishballs + 25/4

so when fishballs = 19
cost = (5/4)(19) + 25/4 = 30 pesos

or

using interpolation

15, 25
19, c
27, 40

(c-25)/(40-25) = (19-15)/(27-15)
(c-25)/15 = 4/12 = 1/3
3c - 75 = 15
3c = 90
c = 30

How did 75/4 + 25/1 became 25/4?

75/4+ 25/1 =175/4
forgive me for my ignorance but it confuses me.

May I ask, how did you get 25 / 4

75/4 + 25/1 = (75+100)/4=25/4

May I ask, where did you get the 75/4? It's confusing me

(5/4)x(15)=75/4

But why did 5/4 retain? near the fishballs

Where did you get 3c?

5/4 is the slope. Thus, it remains

How did 25 become the (b) or y intercept