Line *n* and point *P* are shown on the coordinate plane.

What is the equation of the line parallel to line *n* that passes through point *P*?

A.y=3x+12y=3x+12

B.y=−3x+3y=−3x+3

C.y=3x−6y=3x−6

D.y=−3x−6y=−3x−6

To find the equation of the line parallel to line *n* that passes through point *P*, we need to:

1. Identify the slope of line *n*. Two lines are parallel if and only if they have the same slope.
2. Use the point-slope form of the equation of a line to find the equation of the new line that passes through point *P*.

### Step 1: Find the slope of line *n*
We don't have an explicit representation of line *n*, but we can assume from the answer choices that the slope of line *n* is either 3 or -3 based on the coefficients of *x* in the equations given.

### Step 2: Use the point-slope form
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope of the line, and \( (x_1, y_1) \) is the point the line passes through.

Given the choices, we should identify which option has the correct slope and passes through point *P*. Without the specific coordinates of point *P* or line *n*, let's analyze the structure of each option:

- **Option A**: \( y = 3x + 12 \) – Slope is 3.
- **Option B**: \( y = -3x + 3 \) – Slope is -3.
- **Option C**: \( y = 3x - 6 \) – Slope is 3.
- **Option D**: \( y = -3x - 6 \) – Slope is -3.

Since parallel lines must have the same slope, if line *n* has a slope of either 3 or -3, the correct answer would depend on the slope of line *n* and the coordinates of point *P*.

### Answer:
The answer is the equation with the same slope as line *n*, and it passes through point *P*. Could you provide more information on the slope of line *n* or the coordinates of point *P* so I can confirm the correct equation?

Would you like more details on solving this, or do you have questions?

### Related questions:
1. How do you calculate the slope of a line from two points?
2. What is the point-slope form, and when is it used?
3. How do you determine the y-intercept of a line from its equation?
4. How do you find the equation of a line perpendicular to a given line?
5. How can you determine if two lines are parallel by comparing their slopes?

### Tip:
Two lines are parallel if their slopes are equal. Always check the slope to determine the correct parallel line.

Line n and point P are shown on the coordinate plane. What is the equation of the line parallel to line n that passes through point P? A. y = 3x + 12 B. y = -3x + 3 C. y = 3x - 6 D. y = -3x - 6

Discover how to find the equation of a line parallel to line n that passes through point P on a coordinate plane. This guide explores key concepts like slope, point-slope form, and parallel lines in algebra and coordinate geometry. Ideal for students in Grades 8-10.

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