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To find the point-slope equation of the line, we can use the formula:

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

where:
- \((x_1, y_1)\) is a point on the line,
- \(m\) is the slope of the line.

Given:
- The slope \(m = 2\),
- The point \((x_1, y_1) = (1, 9)\).

Substituting these values into the point-slope form:

\[
y - 9 = 2(x - 1)
\]

This is the point-slope equation of the line.

Would you like a more detailed explanation or have any other questions?

Here are five related questions to explore further:
1. How can you convert the point-slope form to slope-intercept form?
2. What would the equation be if the slope were negative?
3. How do you find the slope if given two points on a line?
4. Can you write the equation of a line parallel to the given line passing through a different point?
5. How would you write the equation in standard form?

**Tip:** Point-slope form is particularly useful for quickly finding the equation of a line when you have one point and the slope.

The slope of the line below is 2. Use the coordinates of the labeled point to find a point-slope equation of the line.

Find the point-slope equation of a line with a given slope of 2 and a labeled point (1, 9). Learn how to apply the point-slope formula step-by-step to determine the equation of the line. This problem covers key concepts in algebra and coordinate geometry. Suitable for students in Grades 8-10.

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