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The problem asks you to write the equation of a line that passes through the point \((6, 1)\) and has a slope \(m = -9\), and to express the equation in **standard form**.

To solve this:

1. Use the **point-slope form** of the equation of a line:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \(m\) is the slope, and \((x_1, y_1)\) is the point on the line.

   Substituting \(m = -9\) and \((x_1, y_1) = (6, 1)\):
   \[
   y - 1 = -9(x - 6)
   \]

2. Simplify the equation:
   \[
   y - 1 = -9x + 54
   \]
   \[
   y = -9x + 55
   \]

3. To convert this to **standard form**, where the equation is of the form \(Ax + By = C\) (with \(A\), \(B\), and \(C\) being integers and \(A\) non-negative):
   \[
   9x + y = 55
   \]

Thus, the equation of the line in standard form is:
\[
9x + y = 55
\]

Would you like more details or further explanation?

Here are 5 questions that expand on this information:
1. How would the equation change if the slope was positive instead of negative?
2. What if the point given was \((0, 0)\), how would the equation look?
3. Can you derive the equation in standard form directly from the slope and point without going through slope-intercept form?
4. How would you find the x-intercept and y-intercept from this equation?
5. What is the general process to convert any linear equation into standard form?

**Tip:** The standard form is particularly useful when you want to find intercepts easily since the x and y terms are on the same side.

Write an equation for the line that passes through the point (6,1) and has a slope of -9. Give the answer in standard form.

Learn how to find the equation of a line passing through the point (6,1) with a slope of -9. This example uses the point-slope form and converts it into standard form (Ax + By = C).

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