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The image you uploaded contains a math problem that involves determining the equation of a line given a point and a slope.

### Problem Statement:
- The question asks for the equation of a line that passes through the point \((2, 1)\) with a slope of \(m = -2\).

### Solution Approach:
To find the equation of the line, we use the **point-slope form** of the equation of a line:
\[
y - y_1 = m(x - x_1)
\]
Where:
- \(m\) is the slope
- \((x_1, y_1)\) is a point on the line

Given:
- \(m = -2\)
- Point: \((x_1, y_1) = (2, 1)\)

Substituting these into the point-slope form:
\[
y - 1 = -2(x - 2)
\]

Now, distribute the slope on the right side:
\[
y - 1 = -2x + 4
\]

Finally, add 1 to both sides to solve for \(y\):
\[
y = -2x + 5
\]

### Conclusion:
The equation of the line is \(y = -2x + 5\).

Based on the image options, the correct choice is \( \boxed{y = -2x + 5} \).

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Do you want more details or have any questions about this solution?

Here are some related questions you might find interesting:
1. How would the equation change if the slope was positive instead of negative?
2. What would be the equation of the line if it passes through the origin with the same slope?
3. How do you convert a point-slope form equation to slope-intercept form?
4. What is the significance of the slope in the equation of a line?
5. Can you derive the equation of a line using two points instead of a point and a slope?

**Tip:** Remember that the point-slope form is particularly useful when you're given a point and a slope directly.

Find the equation of the line that passes through the point (2, 1) with a slope of -2.

Learn how to find the equation of a line that passes through the point (2, 1) with a slope of -2. This problem covers key algebraic concepts, including the point-slope form and slope-intercept form of a linear equation. Suitable for students in Grades 8-10.

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