We are given the equation $-6x + 10y = 20$, and we need to find the equation of a line parallel to this one that passes through the point $(-5, 3)$.

Step 1: Determine the slope of the given line

We first need to write the equation $-6x + 10y = 20$ in slope-intercept form $y = mx + b$, where $m$ is the slope.

Starting with: $-6x + 10y = 20$

Solve for $y$: $10y = 6x + 20$ $y = \frac{6}{10}x + 2$ $y = \frac{3}{5}x + 2$

So, the slope of the given line is $m = \frac{3}{5}$.

Step 2: Equation of the parallel line

A line parallel to the given line will have the same slope $m = \frac{3}{5}$.

We use the point-slope form of the equation of a line: $y - y_1 = m(x - x_1)$ where $(x_1, y_1) = (-5, 3)$ and $m = \frac{3}{5}$.

Substitute the values: $y - 3 = \frac{3}{5}(x + 5)$

Simplify: $y - 3 = \frac{3}{5}x + \frac{15}{5}$ $y - 3 = \frac{3}{5}x + 3$ $y = \frac{3}{5}x + 6$

Step 3: Conclusion

The equation of the parallel line is $y = \frac{3}{5}x + 6$.

Thus, the correct answer is: $\boxed{y = \frac{3}{5}x + 6}$

Would you like further details or have any other questions?

Relative Questions:

1. How can we find the slope of a line given its equation in general form?
2. What is the geometric interpretation of parallel lines with the same slope?
3. How do we convert from point-slope form to slope-intercept form?
4. What is the process to find the equation of a perpendicular line?
5. How does the point-slope formula change if we know the slope and one point?

Tip:

Parallel lines always have the same slope but different intercepts!