Question

For the data in the table, tell whether y varies directly with x . If it does, write an equation for the direct variation.

x y
2 -6.6
3 -9.9
4 -13.2
5 -16.5

yes; y = x – 3.3

no

yes;

yes; y = –3.3x

Answer 1

yes , y = - 3.3x

Explanation:

if y varies directly as x then the equation relating them is

y = kx ← k is the constant of variation , then

k =
`(y)/(x)`

checking k for each ordered pair in the table

`(-6.6)/(2)` = - 3.3

`(-9.9)/(3)` = - 3.3

`(-13.2)/(4)` = - 3.3

`(-16.5)/(5)` = - 3.3

thus k = - 3.3

so y varies directly with x and the equation of direct variation is

y = - 3.3x