If you mean points of (3, 1) and (0, -5) then the slope is 2
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It is: y = -31 and there is no x intercept or slope
If you mean points of (-4, 3) and (3, 1) then the slope is -2/7
The line perpendicular to a line with a slope of 1/5 has a slope of -5.
y = -3x + 5
The slope of a line is undefined if the line is vertical.