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The problem asks to write the equation of a line that is parallel to \( y = \frac{2}{3}x - 3 \) and passes through the point (-3, 1).

### Step 1: Understand the slope of the given line
The equation \( y = \frac{2}{3}x - 3 \) is in slope-intercept form, \( y = mx + b \), where \( m \) is the slope. From this equation, the slope \( m \) is \( \frac{2}{3} \).

### Step 2: Identify that parallel lines have the same slope
Since the new line is parallel to the given line, it will have the same slope. Thus, the slope of the new line is also \( \frac{2}{3} \).

### Step 3: Use point-slope form to find the equation
The point-slope form of a line is given by:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line. Here, \( m = \frac{2}{3} \) and the point is \( (-3, 1) \).

Substitute the values into the point-slope form:
\[
y - 1 = \frac{2}{3}(x - (-3))
\]
\[
y - 1 = \frac{2}{3}(x + 3)
\]

### Step 4: Simplify the equation
Now, simplify the equation:
\[
y - 1 = \frac{2}{3}x + 2
\]
\[
y = \frac{2}{3}x + 2 + 1
\]
\[
y = \frac{2}{3}x + 3
\]

### Final Equation
The equation of the line that is parallel to \( y = \frac{2}{3}x - 3 \) and passes through the point (-3, 1) is:
\[
y = \frac{2}{3}x + 3
\]

Would you like further details or explanations?

Here are five related questions to extend the topic:
1. How do you find the equation of a line that is perpendicular to \( y = \frac{2}{3}x - 3 \)?
2. How would the equation change if the point was (0, 0)?
3. What is the general form of the equation of a line?
4. How can you find the distance between two parallel lines?
5. What are the different forms of a line equation (slope-intercept, point-slope, standard form)?

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

Write the equation of a line that is parallel to y = (2/3)x - 3 and passes through the point (-3, 1).

Find the equation of a line parallel to y = (2/3)x - 3 that passes through the point (-3, 1). This problem explores key concepts like parallel lines, point-slope form, and slope-intercept form. Suitable for students in Grades 8-10.

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