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The problem asks to write an equation of the line that contains the given point (3, -3) and is parallel to the given line \(3x - 7y = 5\).

To solve this:

### Step 1: Rewrite the given line in slope-intercept form
The equation of the line is \( 3x - 7y = 5 \). We solve for \(y\) to get the slope-intercept form \(y = mx + b\), where \(m\) is the slope.

\[
3x - 7y = 5
\]
\[
-7y = -3x + 5
\]
\[
y = \frac{3}{7}x - \frac{5}{7}
\]

So, the slope of the given line is \( m = \frac{3}{7} \).

### Step 2: Use the slope for the new line
Since the new line is parallel to the given line, it will have the same slope, \( m = \frac{3}{7} \). We can now use the point-slope form of the equation to find the equation of the new line.

### Step 3: Apply point-slope form
The point-slope form is given by:

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

Using the point \((3, -3)\) and slope \(m = \frac{3}{7}\):

\[
y - (-3) = \frac{3}{7}(x - 3)
\]
\[
y + 3 = \frac{3}{7}(x - 3)
\]

### Step 4: Simplify
Expand the right-hand side:

\[
y + 3 = \frac{3}{7}x - \frac{9}{7}
\]

Now, subtract 3 from both sides:

\[
y = \frac{3}{7}x - \frac{9}{7} - 3
\]

Convert 3 to a fraction with denominator 7:

\[
y = \frac{3}{7}x - \frac{9}{7} - \frac{21}{7}
\]

Simplify:

\[
y = \frac{3}{7}x - \frac{30}{7}
\]

### Final Answer:
The equation of the line is:

\[
y = \frac{3}{7}x - \frac{30}{7}
\]

Would you like further details or clarification?

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Here are 5 related questions:
1. How would the equation change if the line were perpendicular instead of parallel?
2. What is the y-intercept of the new line?
3. How do you find the slope of a line from a general form equation?
4. Can you convert the final equation to standard form?
5. What is the slope of a vertical or horizontal line?

**Tip:** Remember, lines that are parallel have the same slope.

Write an equation of the line containing the given point (3, -3) and parallel to the line 3x - 7y = 5.

Learn how to write the equation of a line passing through a point (3, -3) and parallel to the line 3x - 7y = 5. This problem covers key concepts such as slope-intercept form and point-slope form, suitable for students in Grades 8-10.

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