Write an equation of the line that passes through (3, 2) and is parallel to the line y=-3x+2.

The equation of a line parallel to another line will have the same slope. The given line is \( y = -3x + 2 \), where the slope is \( -3 \).

For a line parallel to this, we use the point-slope form of the equation of a line:

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

Where:
- \( m \) is the slope of the line (in this case, \( -3 \))
- \( (x_1, y_1) \) is the point the line passes through (in this case, \( (3, 2) \))

Substituting the values:

\[
y - 2 = -3(x - 3)
\]

Now, simplify the equation:

\[
y - 2 = -3x + 9
\]

\[
y = -3x + 11
\]

So, the equation of the line is:

\[
y = -3x + 11
\]

Would you like more details or have any questions? Here are five related questions to expand your understanding:

1. How do you find the equation of a line perpendicular to \( y = -3x + 2 \)?
2. What is the general form of a line's equation?
3. How would the equation change if the line passed through another point?
4. Can you write the equation of a line parallel to \( y = 4x - 7 \)?
5. What is the significance of the slope in parallel lines?

**Tip:** Parallel lines always have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.

Discover how to find the equation of a line parallel to y = -3x + 2 that passes through the point (3, 2). This solution uses key algebraic concepts such as the point-slope and slope-intercept forms. Suitable for students in Grades 8-10.

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