Question

Using the table of ordered pairs, which equation shows the linear relationship between the x and y values? A. y = x + 2 B. y = x - 2 C. y = 2x D. y = -2x

Answer 1

We are given with four linear equations and need to find the best option which shows the relationship between x and y in accordance with the given table . So , for this question as their are three ordered pairs , so it will be long to put all values of x and y in every equation . So , we will be checking only for one ordered pair, let's say be 2nd i.e (1,-2)

Checking for equation one :

`{:\implies \quad \sf y=x+2}`

`{:\implies \quad \sf -2=1+2}`

`{:\implies \quad \sf -2=3}`

As , it's not possible . So this option is wrong

Checking for equation two :

`{:\implies \quad \sf y=x-2}`

`{:\implies \quad \sf -2=1-2}`

`{:\implies \quad \sf -2=-1}`

As , it's not possible . So this option is wrong

Checking for equation three :

`{:\implies \quad \sf y=2x}`

`{:\implies \quad \sf -2=2* 1}`

`{:\implies \quad \sf -2=2}`

As , it's not possible . So this option is wrong

Checking for equation four :

`{:\implies \quad \sf y=-2x}`

`{:\implies \quad \sf -2=-2* 1}`

`{:\implies \quad \sf -2=-2}`

As the fourth equation satisfied the ordered pair ,

Hence , Option D) y = -2x is correct

Answer 2

D. y = -2x

Explanation:

I will be using (-2,4) for all answer choices

a. y = x + 2

4 = -2 + 2

4 = 0

This statement is false

b. y = x - 2

4 = -2 - 2

4 = -4

This statement is false

c. y = 2x

4 = 2(-2)

4 = -4

This statement is false

d. y = -2x

4 = -2(-2)

4 = 4

This statement is true

Therefore, the correct answer is d

Hope this helps!