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?

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.