If the lines shown below (the green and the red lines) are parallel, this means that they have the same slope. This means that they increase by the same factor upward and across; this is why they will never intersect. Slope can be found by finding the change in y values divided by the change in x values, and it represents the rise over run of a line. If two lines have the same slope and the same y-intercept, they are the same line. But, if two lines have the same slope and different y-intercepts, they will be parallel.
Therefore, if the slope of the green line is 3, and the green line is parallel to the red line, then the red line must also have a slope of 3.
Hope this helps!