Question

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?​

Answer 1

Answer: OPTION C

Explanation:

The function of direct variation has this form:

`y=kx`

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:

`(7)/(2)=3.5\\\\(8)/(2)=4`

On Option B:

`(-3)/(2)=-1.5\\\\(-5)/(4)=-1.25`

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":

`k=-2`

This table represents a direct variation.

Answer 2

Option C is correct.

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.