The image shows a math problem that appears to ask for the equation of a line passing through the point (3, 2) and parallel to the line $3x + y - 2 = 0$.

Step-by-Step Solution:

1. Equation of the given line: The given equation is: $3x + y - 2 = 0$ We can rewrite this in slope-intercept form $y = mx + b$, where $m$ is the slope. $y = -3x + 2$ So, the slope of this line is $m = -3$.

2. Slope of the parallel line: Since the lines are parallel, the new line will have the same slope. So, the slope of the new line is also $m = -3$.

3. Equation of the new line: Now we use the point-slope form of the line equation: $y - y_1 = m(x - x_1)$ where $(x_1, y_1)$ is the point the line passes through, and $m$ is the slope. The point given is $(3, 2)$, so: $y - 2 = -3(x - 3)$ Simplifying this: $y - 2 = -3x + 9$ $y = -3x + 11$ So, the equation of the line passing through $(3, 2)$ and parallel to $3x + y - 2 = 0$ is: $y = -3x + 11$ Or, in standard form: $3x + y - 11 = 0$

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Related questions:

1. How do we determine the slope of a line from its equation?
2. What is the difference between parallel and perpendicular lines in terms of their slopes?
3. How can we derive the point-slope form from the slope-intercept form of a line?
4. Can a line passing through the same point have different slopes?
5. How would the equation change if the line were perpendicular instead of parallel?

Tip:

Always express the equation of a line in different forms (like slope-intercept, point-slope, or standard form) for a better understanding of the line's properties.