finding slope: The slope will be the same for a straight line no matter which two points you pick as you know. All you need to do is to calculate the difference in the y coordinates of the 2 points and divide that by the difference of the x coordinates of the points(rise over run). That will give you the slope.
parallel: We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y-intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.
The slope of a line is the rise/run of how far away the points are from each other. Say you have the equation y=3/4x-6, the slope is 3/4 so that means you plot your first point at -6 on the y-axis, because that is your y-intercept, and then you will go up 3, right 4. You will continue to do this until you have enough points to make a line. When two lines are parallel, they will always have the same slope. So the lines y=1/2x+4 and y=1/2x-3 are parallel because not only do they have the same slope, they do not intersect at all, which is a requirement for parallel lines. I hope this helps!!
