To solve this problem, we need to identify a line that is parallel to the given line, $y = \frac{3}{5}x - 7$.

Step 1: Identify the slope of the given line

The equation of the line is in slope-intercept form: $y = mx + b$, where $m$ is the slope. For the given equation: $y = \frac{3}{5}x - 7$ The slope $m$ is $\frac{3}{5}$.

Step 2: Parallel lines have the same slope

To find the line parallel to this, we need another line with the same slope $m = \frac{3}{5}$.

Step 3: Check the provided equations

Let's check the slopes of the provided equations by converting them into slope-intercept form $y = mx + b$.

1. $3x + 5y = 15$: $5y = -3x + 15 \quad \text{(subtract } 3x \text{ from both sides)}$ $y = \frac{-3}{5}x + 3 \quad \text{(divide by 5)}$ The slope is $-\frac{3}{5}$, so this line is not parallel.

2. $5x + 3y = 12$: $3y = -5x + 12 \quad \text{(subtract } 5x \text{ from both sides)}$ $y = \frac{-5}{3}x + 4 \quad \text{(divide by 3)}$ The slope is $-\frac{5}{3}$, so this line is not parallel.

3. $3y - 5x = 6$: $3y = 5x + 6 \quad \text{(add } 5x \text{ to both sides)}$ $y = \frac{5}{3}x + 2 \quad \text{(divide by 3)}$ The slope is $\frac{5}{3}$, so this line is not parallel.

4. $3x - 5y = -30$: $-5y = -3x - 30 \quad \text{(subtract } 3x \text{ from both sides)}$ $y = \frac{3}{5}x + 6 \quad \text{(divide by } -5)$ The slope is $\frac{3}{5}$, which is the same as the given line.

Conclusion:

The line that is parallel to $y = \frac{3}{5}x - 7$ is $3x - 5y = -30$.

Would you like more details or have any questions about this?

Here are five related questions you can explore:

1. What is the general form of a linear equation?
2. How do perpendicular lines' slopes relate to each other?
3. Can we determine the y-intercept of a line from its equation in standard form?
4. What is the process to convert standard form equations to slope-intercept form?
5. How do changes in the slope affect the angle of a line?

Tip: Always ensure that when looking for parallel lines, you focus on comparing their slopes, as that defines their parallel nature.