the slope of a line, given two points P1 and P2 can be found from using the formula (relationship) for the slope of a line (m)
(3,-4) and (-7,10)
m = Δy/Δx = (y2 - y1)/(x2 - x1) = (10 - (-4))/((-7) - 3) = 14/(-10) = -7/5
it doesn't matter which point use choose as P1 or P2...

In order for a line to be perpendicular to any line given i the slope intercept form it must, the slope (m) must be the negative reciprocal of that given.
Thus, if you are given a slope m, any line with a slope -(1/m) will be perpendicular to that line.
In your case, since...

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