A line passes through the points (2,9) and (4,1). What is its equation in point-slope form?

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.

Learn how to find the equation of a line passing through the points (2,9) and (4,1) using the point-slope form. This solution covers the slope calculation and step-by-step explanation of the point-slope equation, suitable for Grades 8-10 students.

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