To graph the equation \( y - 1 = -5(x - 1) \), we need to first rewrite it into slope-intercept form (\( y = mx + b \)).

### Step 1: Expand the equation
\[
y - 1 = -5(x - 1)
\]
Distribute the \(-5\) on the right-hand side:
\[
y - 1 = -5x + 5
\]

### Step 2: Solve for \( y \)
Add 1 to both sides to isolate \( y \):
\[
y = -5x + 6
\]

Now, the equation is in slope-intercept form: \( y = -5x + 6 \), where:
- The slope (\( m \)) is \(-5\), meaning the line goes down 5 units for every 1 unit it moves to the right.
- The y-intercept (\( b \)) is 6, meaning the line crosses the y-axis at \( (0, 6) \).

### Step 3: Plotting the graph
1. **Start at the y-intercept**: Plot the point \( (0, 6) \).
2. **Use the slope**: From \( (0, 6) \), move 1 unit to the right and 5 units down to find another point. This gives the point \( (1, 1) \).
3. **Draw the line**: Connect the two points with a straight line, extending it in both directions.

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### Related Questions:
1. How do you calculate the slope of a line between two points?
2. What does the slope tell you about the steepness of a line?
3. How can you determine the x-intercept of this line?
4. What are other forms of linear equations besides slope-intercept form?
5. How do you graph lines parallel or perpendicular to this one?

**Tip**: When graphing, always check your slope and intercept points to ensure accuracy!

Learn how to graph the linear equation y - 1 = -5(x - 1) by converting it to slope-intercept form. This step-by-step guide covers key concepts such as slope and y-intercept and is suitable for students in Grades 8-10.

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