Final answer:
Option B (2, 5) is the correct solution to the equation y = 3x - 1 since plugging in the x-value 2 into the equation results in the y-value 5.
Step-by-step explanation:
The correct answer is option B. This option can be verified by substituting the x-value of the ordered pair (2, 5) into the equation y = 3x - 1. By multiplying the x-value by 3 and then subtracting 1, we get:
3(2) - 1 = 6 - 1 = 5
The resulting y-value is 5, which matches the y-value of the ordered pair. Hence, option B (2, 5) satisfies the equation. None of the other options produce the correct y-value when their respective x-values are plugged into the equation.
To determine if a point is a solution to an equation, substitute the values of x and y from the point into the equation and check if it is true.
For option A, we have y = 3(4) - 1 = 12 - 1 = 11. Since y does not equal 11, this point is not a solution to the equation y = 3x - 1.
For option B, we have y = 3(2) - 1 = 6 - 1 = 5. Since y equals 5, this point is a solution to the equation y = 3x - 1.
For option C, we have y = 3(4) - 1 = 12 - 1 = 11. Since y does not equal 11, this point is not a solution to the equation y = 3x - 1.
For option D, we have y = 3(0) - 1 = 0 - 1 = -1. Since y equals -1, this point is a solution to the equation y = 3x - 1.