Let's analyze the equation provided in the image and break down the steps for graphing it.

Equation:

$y - 1 = 3(x - 2)$

Step-by-Step Solution:

1. Simplify the equation: $y - 1 = 3(x - 2)$ Distribute the 3 on the right-hand side: $y - 1 = 3x - 6$ Add 1 to both sides: $y = 3x - 5$ This is now in slope-intercept form $y = mx + b$, where $m = 3$ (the slope) and $b = -5$ (the y-intercept).

2. Plot the y-intercept: The y-intercept is the point where the line crosses the y-axis. Since $b = -5$, the line crosses the y-axis at $(0, -5)$. This is one point on the line.

3. Use the slope to find another point: The slope $m = 3$ means the line rises 3 units for every 1 unit it moves to the right. Starting from the y-intercept $(0, -5)$:

   • Move 1 unit to the right (x increases by 1).
   • Move 3 units up (y increases by 3).

   This gives us the point $(1, -2)$.

4. Draw the line: Now that we have two points: $(0, -5)$ and $(1, -2)$, plot these points and draw a straight line through them.

The line you draw will be the graph of the equation $y = 3x - 5$.

Would you like more details on any step or have additional questions?

Additional Related Questions:

1. What are other ways to graph a linear equation besides using the slope-intercept form?
2. How do you convert a linear equation into slope-intercept form?
3. What does the slope of a line represent in real-world situations?
4. How would you graph a line if given the standard form $Ax + By = C$?
5. Can you explain how the y-intercept affects the position of the line on the graph?

Tip: Always check the accuracy of your graph by substituting points back into the equation.