https://file.aiquickdraw.com/mathbot/file/1728597325017ic4324s9.jpg

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.

Learn how to graph the linear equation y - 1 = 3(x - 2) by simplifying it into slope-intercept form and using key graphing techniques such as plotting the y-intercept and applying the slope. Suitable for students in Grades 8-10.

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