TheLordCommander wrote:
my question is - we calculated the intersections in the y axis between 9 and -25 to get the answer; why did we not calculate the intersections in the x axis between -15 and 5 instead? Please bear with me if this is a stupid question. Thank you.
Dear
TheLordCommander,
I'm happy to respond.
This is a hard question, so questions about it are not "stupid."
Part of the requirement of the question is that the y-intercept has to be an integer. If we mark off the boundaries on the y-intercept, then we simply can count integers along the y-axis.
You see, if the x-intercept is an integer, that doesn't guarantee that the y-intercept is an integer (unless the slope is +1 or -1). Certainly for any non-integer slope, the general rule is that for most x-intercepts that
are integers, the y-intercept is
not an integer, and vice versa. If we start looking at points on the x-axis, we know they have to be -15 and 5, but within that range, we have no idea what spacings of the values of the x-intercept would result in integer values on the y-intercept.
Therefore, it's much easier simply to stick to the y-intercept and count integers.
Does all this make sense?
Mike
Makes a lot of sense Mike. Thanks