https://file.aiquickdraw.com/mathbot/file/1726177651442mwnjcdf9.jpg

The equation you need to graph is:

\[
y - 2 = -3(x - 1)
\]

Let's first rewrite this equation in slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

### Step 1: Simplify the given equation
Start with:
\[
y - 2 = -3(x - 1)
\]
Distribute the \(-3\) on the right-hand side:
\[
y - 2 = -3x + 3
\]
Now, add 2 to both sides to isolate \(y\):
\[
y = -3x + 5
\]

### Step 2: Identify the slope and y-intercept
- Slope (\(m\)): \(-3\)
- y-intercept (\(b\)): 5

### Step 3: Plot the graph
- The y-intercept is the point where the line crosses the y-axis, at \((0, 5)\).
- The slope tells you that for every 1 unit increase in \(x\), \(y\) decreases by 3 units (since the slope is negative).

### Step 4: Draw points
- Start at \((0, 5)\) for the y-intercept.
- From \((0, 5)\), move 1 unit to the right (positive \(x\)-direction), and 3 units down (negative \(y\)-direction). This gives the point \((1, 2)\).
- Continue this pattern to find more points.

Once you plot these points, draw a straight line through them to represent the equation.

Would you like further assistance with the graph or more details?

### Related Questions:
1. How do you convert other forms of equations into slope-intercept form?
2. What is the significance of the slope in linear equations?
3. How do you find the x-intercept of a line from an equation?
4. What happens when the slope is zero or undefined?
5. How can you graph a line when given the slope and a single point?

### Tip:
Always check the signs of the slope and y-intercept carefully when plotting.

Learn how to graph the linear equation y - 2 = -3(x - 1) by converting it into slope-intercept form and identifying the slope and y-intercept. Suitable for students in Grades 7-10.

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