The given equation is:

\[
y - 6 = \frac{4}{5}(x - 3)
\]

To graph this, let's follow these steps:

### Step 1: Rewrite in slope-intercept form (y = mx + b)
We'll distribute \(\frac{4}{5}\) and solve for \(y\).

\[
y - 6 = \frac{4}{5}x - \frac{4}{5} \times 3
\]
\[
y - 6 = \frac{4}{5}x - \frac{12}{5}
\]
Now, add 6 to both sides:
\[
y = \frac{4}{5}x - \frac{12}{5} + 6
\]
Convert 6 to a fraction:
\[
6 = \frac{30}{5}
\]
So the equation becomes:
\[
y = \frac{4}{5}x + \frac{18}{5}
\]

Now, the equation is in slope-intercept form, \(y = mx + b\), where:
- \(m = \frac{4}{5}\) is the slope,
- \(b = \frac{18}{5}\) is the y-intercept.

### Step 2: Identify the slope and y-intercept
- **Slope (m):** \(\frac{4}{5}\), which means that for every 5 units you move horizontally (right), you move 4 units vertically (up).
- **Y-intercept (b):** \(\frac{18}{5}\), which is approximately 3.6.

### Step 3: Plot the y-intercept
Start by plotting the y-intercept \(\left(0, \frac{18}{5}\right)\) or approximately \((0, 3.6)\).

### Step 4: Use the slope to plot another point
From \((0, 3.6)\), move 5 units to the right and 4 units up. This gives another point on the graph.

### Step 5: Draw the line
Draw a straight line through the points.

Would you like more details or have any questions about the process?

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Here are 5 related questions to deepen your understanding:

1. How do you convert an equation from point-slope form to slope-intercept form?
2. What does the slope of a line represent in real-world contexts?
3. How can you find the x-intercept of the line \(y = \frac{4}{5}x + \frac{18}{5}\)?
4. What is the general form of a linear equation, and how does it differ from slope-intercept form?
5. How can you graph a line if given two points instead of the equation?

**Tip:** When graphing lines, always pay attention to both the slope and the intercepts—they help you quickly and accurately sketch the graph!

Learn how to graph the linear equation y - 6 = 4/5(x - 3) by converting it to slope-intercept form. This problem covers essential algebraic concepts, including slope, intercepts, and plotting linear equations. Suitable for students in Grades 8-10.

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