. The number of drops of red tint needed to make a certain shade of purple paint varies directly with the number of gallons of paint base. Suppose that 5 drops of red tint can be mixed with 2 gallons of paint base to create the correct shade. How many drops of red tint must be mixed with 6 gallons of paint base to create the correct shade?

15 drops of red tint must be mixed with 6 gallons of paint base to create the correct shade

Step-by-step explanation:

The number of drops of red tint needed to make a certain shade of purple paint varies directly with the number of gallons of paint base.

This is expressed Mathematically as:

= R ∝ P

Where R = Red paint

P = Paint base

R = kP

Suppose that 5 drops of red tint can be mixed with 2 gallons of paint base to create the correct shade.

Hence

5 = 2k

k = 5/2

How many drops of red tint must be mixed with 6 gallons of paint base to create the correct shade?

This is calculated as:

R = kP

Where k = 5/2

Hence:

R = 5/2 × 6

R = 15 drops of red tint

Hence, 15 drops of red tint must be mixed with 6 gallons of paint base to create the correct shade.

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.