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The problem asks for the equation of a line in point-slope form, given a slope of \(-6\) and the point \((7, 1)\) through which the line passes.

The point-slope form of the equation of a line is:

\[
y - y_1 = m(x - x_1)
\]

Where:
- \( m \) is the slope of the line,
- \( (x_1, y_1) \) is the point through which the line passes.

In this case:
- \( m = -6 \),
- \( x_1 = 7 \),
- \( y_1 = 1 \).

Substitute these values into the point-slope form:

\[
y - 1 = -6(x - 7)
\]

This is the equation in point-slope form.

Would you like any further explanation or details? 

Here are five questions to expand this concept:
1. How can you convert the point-slope form to slope-intercept form?
2. What is the difference between point-slope form and slope-intercept form?
3. How would the equation change if the slope was positive instead of negative?
4. Can you derive the same equation using two points instead of one?
5. How would the graph of this line look based on the equation?

**Tip:** Always remember to simplify fractions when working with point-slope form for easier interpretation of the equation.

A line with a slope of -6 passes through the point (7, 1). What is its equation in point-slope form?

Find the equation of a line with slope -6 passing through the point (7, 1) in point-slope form. This problem involves the point-slope form equation, perfect for students in Grade 8-10 learning about linear equations.

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