We are given the equation $y = 3x - 1$ and asked to determine which of the ordered pairs is a solution to this equation.

Let's test both pairs by substituting the $x$ values into the equation and checking if the corresponding $y$ values satisfy it.

1. Pair $(2, 7)$:

Substitute $x = 2$ into the equation: $y = 3(2) - 1 = 6 - 1 = 5$ The equation gives $y = 5$, but the ordered pair has $y = 7$, so $(2, 7)$ is not a solution.

2. Pair $(4, 11)$:

Substitute $x = 4$ into the equation: $y = 3(4) - 1 = 12 - 1 = 11$ The equation gives $y = 11$, which matches the ordered pair's $y$-value. Therefore, $(4, 11)$ is a solution.

Answer:

The ordered pair $(4, 11)$ is the solution.

Would you like more details or have any further questions?

Here are 5 related questions for further practice:

1. What is the slope of the equation $y = 3x - 1$?
2. How can you determine if an ordered pair is a solution to a linear equation?
3. What is the y-intercept of the equation $y = 3x - 1$?
4. Can you find another ordered pair that is a solution to $y = 3x - 1$?
5. How would the graph of $y = 3x - 1$ look?

Tip: For any linear equation of the form $y = mx + b$, the value of $m$ is the slope, and $b$ is the y-intercept!