There's absolutely no connection or correlation whatsoever
between the steepness and the direction of a slope.
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For a positive number, as the slope(y=mx+b where m is the slope) gets greater in value, the line gets steeper when plotted on a graph. For a negative number, as the slope(y=mx+b where m is the slope) gets greater in value, the line gets less steep when plotted on a graph.
Never.
if the line slants down (from left to right) then it is negative. if the line slants up (from left to right) then it is positive. horisontal lines have a slope of "0" and and vertical ones are undefined.
Not always because it can also be negative
Integers are whole numbers that go from negative infinity to positive infinity. As such, they do cover the negative range of the number line.