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To determine the equation of the line that passes through the points \((9, 8)\) and \((6, 4)\), we can follow these steps:

1. **Find the slope (m)** of the line using the formula:
   \[
   m = \frac{y_2 - y_1}{x_2 - x_1}
   \]
   Where \((x_1, y_1) = (9, 8)\) and \((x_2, y_2) = (6, 4)\).

   Substituting the values:
   \[
   m = \frac{4 - 8}{6 - 9} = \frac{-4}{-3} = \frac{4}{3}
   \]

2. **Use the point-slope form of the equation** of a line:
   \[
   y - y_1 = m(x - x_1)
   \]
   Let's use the point \((9, 8)\) to plug in for \(x_1\), \(y_1\), and \(m = \frac{4}{3}\):
   \[
   y - 8 = \frac{4}{3}(x - 9)
   \]

3. **Simplify the equation**:
   \[
   y - 8 = \frac{4}{3}x - 12
   \]
   Add 8 to both sides:
   \[
   y = \frac{4}{3}x - 4
   \]

So, the equation of the line is:
\[
y = \frac{4}{3}x - 4
\]

Would you like any further clarification or details on this?

Here are five related questions you might want to explore:
1. How can you verify the equation of the line using a graph?
2. How do you find the x- and y-intercepts from the equation of a line?
3. Can you derive the equation of a line from different forms, such as the standard form?
4. How would the equation change if the points were swapped?
5. How can you find the distance between the two points?

**Tip**: Always double-check your slope calculation, as it is key to determining the correct equation of the line!

Graph the line that passes through the points (9, 8) and (6, 4) and determine the equation of the line.

Learn how to find the equation of a line passing through two points (9, 8) and (6, 4). This solution involves calculating the slope and using the point-slope form, simplifying into the slope-intercept form.

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