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!