Question

for the data in the table, does y vary directly with x? if it does write an equation for the direct variation.x: 8, 16, 24 y: 13, 26, 39
a. yes; y=5x
b. yes; y=10x
c. yes; y=1.625x
d. no; y does not vary directly with x

Answer 1

Definition of Directly proportional: as one amount increases, another amount increases at the same rate.

To find the rate, use rise/run (change in y/change in x).
(26-13)/(16-8)=13/8
(39-26)/(24-16)=13/8

It seems it is increasing at the same rate, so y varies directly with x at the rate of 13/8 = 1.625.