Answer:
constant of variation (k) = 6
Step-by-step explanation:
Let us first represent the sentence in direct variation expression:
"the gallons of water used to take a shower varies directly with the number of minutes in the shower"
Let the gallons of water used = g
Let the number of minutes spent in the shower = m
g ∝ m
where: ∝ = sign of proportionality
This means that as g increases, m increases also, and the same holds for decrease too.
g ∝ m
g = km
where k = constant of variation ( or proportionality constant)
Next, If a 6-minute shower uses 36 gallons of water, find the constant of variation
g = 36 gallons
m = 6 minutes
∴ g = km
= 36 = k × 6
k = 36 ÷ 6 = 6
k = 6
