To find the equation of a line passing through the points $(2, 9)$ and $(4, 1)$ in point-slope form, we follow these steps:

1. Find the slope (m) using the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 9}{4 - 2} = \frac{-8}{2} = -4$

2. Use the point-slope form of a line equation:

$y - y_1 = m(x - x_1)$

You can use either point for $(x_1, y_1)$. Let's use the point $(2, 9)$:

$y - 9 = -4(x - 2)$

Thus, the equation of the line in point-slope form is:

$y - 9 = -4(x - 2)$

Would you like more details on the steps, or have any questions?

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Here are five related questions to explore this concept further:

1. How do you convert the point-slope form into slope-intercept form?
2. What is the equation of the line if you use the point $(4, 1)$ in the point-slope formula?
3. How do you find the x-intercept of the line?
4. How do you find the y-intercept of the line using the given points?
5. What happens to the equation if the slope was positive instead of negative?

Tip: The point-slope form is very useful when you already know a point on the line and the slope. It directly shows how the line changes relative to that point.