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.

Would you like me to generate a visual graph of this equation for you?

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!