The slope of a line in the form $Ax + By = C$ (called the standard form) can be determined by converting the equation to the slope-intercept form $y = mx + b$, where $m$ is the slope.

Let's rewrite the given equation:

$-2x + y = -7$

Solve for $y$ by isolating it on one side:

$y = 2x - 7$

Now the equation is in slope-intercept form, and the slope $m$ is the coefficient of $x$. So, the slope of this line is $m = 2$.

Parallel lines have the same slope. Therefore, the slope of any line parallel to this one is also $2$.

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Would you like more details on this or have any additional questions? Here are some related questions to consider:

1. What is the slope of a line perpendicular to this one?
2. How do you find the y-intercept of a line in slope-intercept form?
3. Can you find the equation of a line parallel to this one passing through a specific point?
4. What is the general formula for the slope of a line given two points?
5. How do parallel and perpendicular slopes relate to each other geometrically?

Tip: The slope of a line describes its steepness and direction—positive slopes rise, while negative slopes fall.