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Isn't it wrong to assume the following:
A line with a positive slope (always) passes through the first and the third quadrant
while a line with a negative slope (always) passes through the second and the fourth quadrant.
I mean you could have a line with a positive slope that looks like x=-100 but
really isn't 'cause it's slightly tilted to the right. So, this line is definitely not vertical though
it covers the same quadrants as x=-100 does, that is, the second and the third quadrant.
And the same reasoning applies to the one with a negative slope. For example, a line that's slanted a little bit to the left compared with a vertical line, x = 100, passes through the first and the fourth quadrant.
So basically, you can say for sure the above statement is correct if you know that the line passes through the origin. Otherwise, it could be true, but maybe not - which means
a line with a positive slope would have to pass at least one of the two quadrants (if not both 1 and 3), and ditto for the one with a negative slope: Both 2 & 4, OR
if not 2 then definitely 4, and vice versa.
Please confirm, thank you.
JJ
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