The problem asks which of the provided graphs represents the equation $y - 2 = 3(x - 1)$, which is in point-slope form.

1. Rewrite the equation into slope-intercept form: $y - 2 = 3(x - 1)$ Distribute the 3: $y - 2 = 3x - 3$ Add 2 to both sides to isolate $y$: $y = 3x - 1$ So the equation in slope-intercept form is $y = 3x - 1$, where the slope (m) is 3 and the y-intercept is -1.

2. Identify the key characteristics:

   • Slope: The line has a slope of 3, meaning it rises 3 units for every 1 unit it moves to the right.
   • Y-intercept: The line crosses the y-axis at $y = -1$.

3. Now check the graphs:

   • Graph A: This line does not pass through $y = -1$.
   • Graph B: This line has a slope of 3 and passes through the y-axis at $y = -1$. This is a good candidate.
   • Graph C: This line does not have the correct slope.
   • Graph D: This line has the correct slope but crosses the y-axis at $y = 1$, which is incorrect.

Thus, Graph B is the correct graph.

Would you like further details or have any questions?

Here are five follow-up questions you might consider:

1. How do you convert a point-slope form equation to slope-intercept form?
2. How can you determine the slope of a line from a graph?
3. What is the general form of the point-slope equation?
4. How can you find the y-intercept of a line from its equation?
5. How would the graph change if the slope was negative?

Tip: When graphing a line, always start by identifying the slope and the y-intercept for easier plotting!