Find the slope of a line parallel to the line whose equation is 6, x, minus, 10, y, equals, minus, 1006x−10y=−100. Fully simplify your answer

1. Break Down the Problem

To find the slope of a line parallel to the given line, we first need to determine the slope of the given line from its equation.

2. Relevant Concepts

The slope-intercept form of a line is given by the equation:
$y = mx + b$
where $m$ is the slope. We will rearrange the provided equation into this form to identify the slope.

3. Analysis and Detail

The given equation is:
$6x - 10y = -100$
We will rearrange this to isolate $y$:

1. Start by moving $6x$ to the right side:
   $-10y = -6x - 100$

2. Now, divide each term by -10 to solve for $y$:
   $y = \frac{6}{10}x + 10$
   or simplifying further:
   $y = \frac{3}{5}x + 10$

Now, we can identify the slope $m$ of the line, which is:
$m = \frac{3}{5}$

Since parallel lines have the same slope, the slope of any line parallel to this one will also be:
$m_{parallel} = \frac{3}{5}$

4. Verify and Summarize

We verified the calculations and confirmed that the slope of the line parallel to the given line is indeed $\frac{3}{5}$.

Final Answer

The slope of a line parallel to the line whose equation is $6x - 10y = -100$ is $\frac{3}{5}$.