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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.

Which equation represents a line which is parallel to the line y = (3/5)x - 7?

Learn how to determine which equation represents a line that is parallel to y = (3/5)x - 7. This example uses algebraic concepts such as slopes and linear equations in standard and slope-intercept form. Suitable for Grades 8-10.

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