a) Equation 'a' has a proportional relationship.
b) Equation 'b' does not have a proportional relationship.
c) Table 'c' does not have a proportional relationship.
d) Table 'd' has a proportional relationship.
A proportional relationship exists when two variables increase or decrease at a constant ratio.
a) C = 1.45n has a constant ratio of 1.45 and represents a proportional relationship.
b) y = 2x + 6 does not have a constant ratio because y increases more than x based on the y-intercept 6.
c)
Cake 0.125 0.5 1 2
Price $1.25 $6 $12 $24
Ratio 10 (1.25/0.125) 12 (6/0.5) 12 (12/1) 12 (24/2)
d)
Liters 1 2 3 5
Miles 30 60 90 150
Ratio 30 (30/1) 30 (60/2) 30 (90/3) 30 (150/5)
Thus, we can conclude that equation A and table D have proportional relationships while equation B and table C have proportional relationships.