https://file.aiquickdraw.com/mathbot/file/1728305893721cmjh0rer.jpg

The equation provided in the image is:

\[
y - 2 = -4(x - 1)
\]

We will convert this to slope-intercept form \(y = mx + b\) where \(m\) is the slope and \(b\) is the y-intercept.

### Step 1: Distribute the \(-4\) on the right-hand side
\[
y - 2 = -4(x - 1) \implies y - 2 = -4x + 4
\]

### Step 2: Add 2 to both sides to solve for \(y\)
\[
y = -4x + 4 + 2 \implies y = -4x + 6
\]

Now, the equation is in slope-intercept form:

\[
y = -4x + 6
\]

- **Slope (m):** -4
- **Y-intercept (b):** 6

### Graphing:
1. Start by plotting the y-intercept, which is the point \((0, 6)\).
2. Use the slope \(-4\), which means "down 4 units for every 1 unit to the right," to plot the next points.

#### Example Points:
- From \((0, 6)\), move down 4 units and right 1 unit to plot the point \((1, 2)\).
- Repeat to plot other points like \((2, -2)\), \((3, -6)\), and so on.

Once the points are plotted, draw a straight line through them to represent the equation \(y = -4x + 6\).

---

Do you need more details or have any other questions?

Here are 5 related questions to consider:
1. How do you interpret the slope of a line in real-world problems?
2. What happens to the graph if the slope changes but the y-intercept stays the same?
3. Can you graph a line without first converting to slope-intercept form?
4. What are other forms of linear equations besides slope-intercept form?
5. How do you find the equation of a line given two points?

**Tip:** Always check the direction of the slope. A negative slope means the line goes downward from left to right!

Learn how to graph the linear equation y - 2 = -4(x - 1) by converting it into slope-intercept form (y = mx + b). Explore key algebraic concepts, such as identifying slope and y-intercept, and practice graphing a straight line. Suitable for students in Grades 8-10.

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