Question

Item 20 A bathtub is draining at a constant rate. After 2 minutes, it holds 30 gallons of water. Three minutes later, it holds 12 gallons of water. Write an equation that represents the number y of gallons of water in the tub after x minutes

Answer 1

Y=mx+c since its at constant rate
at (30,2)
30=m2+c-----(1)
at(12,3)
12=m3+c-----(2)
by multiplying (2)by 2.5,
30=7.5m+2.5c-----(3)
by comparing (1) and (3)
2m+c=7.5m+2.5c
5.5m+1.5c=0
5.5m=-1.5c
m=-1.5/5.5c----(4)
sub 4 into 1,
-6/11c+c=30
c=66
m=-1.5/5.5*66=-18
Equation : y=-18x+66

u can try substituting back 2min and 3 mins to verify it works