Which of (3, 5), (4, 6), (5, 7), and (6, 8) are solutions to y = x + 2?
To check whether a point is a solution to a given equation, we substitute the values of x and y into the equation and see if they are equal.
For the point (3, 5):
y = x + 2
5 = 3 + 2
5 = 5
Since the equation is true when we substitute (3, 5), it is a solution.
For the point (4, 6):
y = x + 2
6 = 4 + 2
6 = 6
Since the equation is true when we substitute (4, 6), it is a solution.
For the point (5, 7):
y = x + 2
7 = 5 + 2
7 = 7
Since the equation is true when we substitute (5, 7), it is a solution.
For the point (6, 8):
y = x + 2
8 = 6 + 2
8 = 8
Since the equation is true when we substitute (6, 8), it is a solution.
Therefore, all of the given points (3, 5), (4, 6), (5, 7), and (6, 8) are solutions to the equation y = x + 2.
To determine which ordered pairs are solutions to the equation y = x + 2, we can substitute the x and y values from each pair into the equation and see if the equation holds true.
1. For (3, 5):
Substituting x = 3 and y = 5 into y = x + 2:
5 = 3 + 2
5 = 5
Since the equation holds true, (3, 5) is a solution to y = x + 2.
2. For (4, 6):
Substituting x = 4 and y = 6 into y = x + 2:
6 = 4 + 2
6 = 6
Again, the equation holds true, so (4, 6) is a solution.
3. For (5, 7):
Substituting x = 5 and y = 7 into y = x + 2:
7 = 5 + 2
7 = 7
The equation holds true, so (5, 7) is a solution.
4. For (6, 8):
Substituting x = 6 and y = 8 into y = x + 2:
8 = 6 + 2
8 = 8
Once again, the equation holds true, so (6, 8) is a solution.
Therefore, all four ordered pairs (3, 5), (4, 6), (5, 7), and (6, 8) are solutions to y = x + 2.
To determine whether each pair in the set {(3,5), (4,6), (5,7), (6,8)} is a solution to the equation y = x + 2, we can substitute the values of x and y into the equation and see if they satisfy the equation.
Let's go through each pair one by one:
For (3, 5):
Substituting x = 3 and y = 5 into the equation y = x + 2:
5 = 3 + 2
5 = 5
Since the equation is satisfied, (3, 5) is a solution to y = x + 2.
For (4, 6):
Substituting x = 4 and y = 6 into the equation y = x + 2:
6 = 4 + 2
6 = 6
Again, the equation is satisfied, so (4, 6) is a solution to y = x + 2.
For (5, 7):
Substituting x = 5 and y = 7 into the equation y = x + 2:
7 = 5 + 2
7 = 7
The equation is satisfied, so (5, 7) is a solution to y = x + 2.
For (6, 8):
Substituting x = 6 and y = 8 into the equation y = x + 2:
8 = 6 + 2
8 = 8
Once again, the equation is satisfied, so (6, 8) is a solution to y = x + 2.
In summary, all four pairs (3, 5), (4, 6), (5, 7), and (6, 8) are solutions to the equation y = x + 2.