Which table represents a direct variation function?
a.
input (x)23456
output (y)7891011
b.
input (x)246810
output (y)-3-5-6-7-8
c.
input (x)-5-4-3-2-1
output (y)108642
d.
input (x)-21012
output (y)-3-3-3-3-3
is it a?

Option C is correct.

Step-by-step explanation:

A direct variation function is

y/x = k

i.e. we can say that the ratio of y and x is equal to a constant value k.

We will check for each Option given.

Option A

7/2 = 7/2

8/3 = 8/3

9/4 = 9/4

10/5 = 2

11/6 = 11/6

Option D is incorrect as y/x ≠ k as ratio of y/x for each value of table doesn't equal to constant

Option B

-3/2 = -3/2

-5/4 = -5/4

-6/6 = -1

-7/8 = -7/8

-8/10 = -4/5

Option B is incorrect as y/x ≠ k as ratio of y/x for each value of table doesn't equal to constant

Option C

10/-5 = -2

8/-4 = -2

6/-3 = -2

4/-2 = -2

2/-1 = -2

Option C is correct as y/x = k as ratio of y/x for each value in table c is equal to constant value -2

Option D

-3/-2 = 3/2

-3/1 = -3

-3/0 = 0

-3/1 = -3

-3/2 = -3/2

Option D is incorrect as y/x ≠ k as ratio of y/x for each value of table doesn't equal to constant .

SO, Option C is correct.

OPTION C

Step-by-step explanation:

The function of direct variation has this form:

Where k is the constant of variation.

Let's  check if there is a constant of variation on the Options "a" and "b":

On Option A:

On Option B:

There is no constant of variation, then these tables do no represent a direct variation.

On the table shown in Option "d" you can observe that "y" does not change when "x" changes. Then it does not represent a direct variation.

Since on the table shown in Option "c":

 This table represents a direct variation.

the above table 1 will calculate the population size (n) after a certain length of time (t). all you need to do is plug in the initial population number (no), the growth rate (r) and the length of time (t). the constant (e) is already entered into the equation. it stands for the base of the natural logarithms (approximately 2.71828). growth rate (r) and time (t) must be expressed in the same unit of time, such as years, days, hours or minutes. for humans, population growth rate is based on one year. if a population of people grew from 1000 to 1040 in one year, then the percent increase or annual growth rate is 40/1000 x 100 = 4 percent.

step-by-step explanation: