Question

The graph of the equation y − 1 = −2(x − 2) contains which set(s) of ordered pairs? Select all that apply.

A. (0, −2) and (1, 3)
B. (0, 5) and (−2, 9)
C. (−1, 7) and (2, 1)
D. (3, −1) and (2, −1)

Answer 1

B. (0, 5) and (−2, 9).

C. (−1, 7) and (2, 1).

Explanation:

We have given an equation y − 1 = −2(x −2).

We need to find the solutions of this given equation in sets of ordered pair.

We know that,

The equation y − 1 = −2(x −2).

From option B) (0, 5) and (−2, 9).

y − 1 = −2(x-2)

Putting the value of x and y from the first pair (0,5)

5-1 = -2(0-2)

4 = 0+4

4 = 4

Putting the value of x and y from (-2,9)

9-1 = -2(-2-2)

8 = 4+4

8 = 8

From option C), (−1, 7) and (2,1).

Putting the value of x and y from (−1, 7),

7-1 = -2(-1-2)

6 = 2+4

6 = 6

Putting the value of x and y from (2,1),

1-1 = -2(2-2)

0 = -2(0)

0 = 0

So, we can see that the both pair of option B and option C is completely solve the equation y − 1 = −2(x −2).

Answer 2

OPTION B.

OPTION C.

Explanation:

Given the equation of the line:

`y - 1 = -2(x -2)`

We can substitute the coordinates of each set of ordered pairs into the equation in order to know which belong to the graph of that equation:

A.
`(0, -2)\ and\ (1, 3)`

Substituting into the equation these coordinates:

`x=0\\\\y=-2`

We get:

`-2 - 1 = -2(0 -2)\\\\-3\\eq 4`

The graph of the given line does not contain this set of ordered pairs.

B.
`(0, 5)\ and\ (-2, 9)`

Substituting into the equation these coordinates:

`x=0\\\\y=5`

We get:

`5 - 1 = -2(0 -2)\\\\4=4`

Substituting into the equation the coordinates of the other ordered pair:

`x=-2\\\\y=9`

We get:

`9 - 1 = -2(-2 -2)\\\\8=8`

The graph of the given line contains this set of ordered pairs.

C.
`(-1, 7)\ and\ (2, 1)`

Substituting into the equation these coordinates:

`x=-1\\\\y=7`

We get:

`7- 1 = -2(-1 -2)\\\\6=6`

Substituting into the equation the coordinates of the other ordered pair:

`x=2\\\\y=1`

We get:

`1 - 1 = -2(2 -2)\\\\0=0`

The graph of the given line contains this set of ordered pairs

D.
`(3, -1)\ and\ (2, -1)`

Substituting into the equation these coordinates:

`x=3\\\\y=-1`

We get:

`-1 - 1 = -2(3 -2)\\\\-2=-2`

Substituting the other ordered pais (2, -1):

`-1 - 1 = -2(2 -2)\\\\-2\\eq 0`

The graph of the given line does not contain this set of ordered pairs.