The collections of ordered pairs that correspond to the graph of the equation y − 1 = −2(x − 2) includes:
- (0, 5) and (−2, 9)
- (−1, 7) and (2, 1)
Answer: Options B and C
Step-by-step explanation:
Starting with the equation of the line y - 1 = -2 (x - 2), we can manipulate this equation into
y = - 2 x + 5
Now, by substituting the coordinates of each pair of ordered pairs provided, we can determine which pairs are contained within the graph of this equation.
A.(0, -2) and (1, 3)
-2 = -2(0) + 5 results in -2 = 5
3 = -2(1) + 5 results in 3 = 3 and confirms it's not part of the ordered pairs set.
B. (0, 5) and (−2, 9)
5 = -2(0) + 5 results in 5 = 5
9 = -2(-2) + 5 results in 9 = 9 confirming these ordered pairs do belong.
C. (−1, 7) and (2, 1)
7 = -2(-1) + 5 results in 7 = 7
1 = -2(2) + 5 results in 1 = 1 confirming these pairs are included as well.
D. (3, −1) and (2, −1)
-1 = -2(3) + 5 gives -1 = -1
-1 = -2(2) + 5 gives -1 = 1 confirming these pairs do not belong.
E. (1, 2) and (4, 3)
2 = -2(1) + 5 results in 2 = 3
3 = -2(4) + 5 results in 3 = -3 confirming these do not belong.
Therefore, it can be concluded that options B and C satisfy the equation as substituting values for x and y verifies their compliance with the given expression.
