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Part 1
Graph the equation.
y−2=−4​(x−2​)

Given the equation: 

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

### Step 1: Rewrite in Slope-Intercept Form
The equation is currently in point-slope form, \(y - y_1 = m(x - x_1)\). To rewrite it in the slope-intercept form \(y = mx + b\):

1. Expand the right side:
   
   \[
   y - 2 = -4(x - 2)
   \]

   Distribute the \(-4\):

   \[
   y - 2 = -4x + 8
   \]

2. Add 2 to both sides to isolate \(y\):

   \[
   y = -4x + 10
   \]

Now, the equation is in slope-intercept form, where the slope \(m = -4\) and the y-intercept \(b = 10\).

### Step 2: Plot the Graph
1. **Plot the y-intercept**: Start by plotting the point \((0, 10)\) on the graph.
2. **Use the slope**: The slope \(-4\) means that for every 1 unit you move to the right (positive x-direction), you move 4 units down (negative y-direction). From \((0, 10)\):
   - Move 1 unit right to \(x = 1\) and 4 units down to \(y = 6\), giving the point \((1, 6)\).
   - Repeat to get more points if needed.

3. **Draw the line**: Connect these points to form a straight line.

Would you like a detailed graphical plot for this equation, or do you have any further questions?

### 5 Related Questions to Expand Understanding
1. What is the point-slope form of a linear equation and how is it useful?
2. How do you convert a linear equation from point-slope form to slope-intercept form?
3. What does the slope of a line represent in a graph, and how can it be interpreted in real-world scenarios?
4. How do changes in the slope affect the steepness of the line on a graph?
5. How would the graph of the equation change if the slope were positive instead of negative?

### Tip
Always plot the y-intercept first when graphing a line from its slope-intercept form, then use the slope to find additional points. This method helps keep the graph accurate.

Graph the equation y − 2 = −4(x − 2)

Learn how to graph the linear equation y − 2 = −4(x − 2). This step-by-step solution covers converting from point-slope form to slope-intercept form and explains how to plot key points on a graph. Suitable for students in Grades 8-10.

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