laugh all you want, i dont care… but for the first time, since i learnt y=mx+c 12 yrs ago, i actually understand what it means… i can actually put it into a sentence and mathematically explain what y=mx+c means!!!
all thanks to this crazy maths collegue, and this paper which brought the enlighting moment….. when i went, “so thats what it means!”
so…. the idea is that this equation actually describes motion, for example a displacement-time graph…
if you look at the scribbled paper, it contains a table, which corrosponds to the equation y=2x+5….
we were actually talking abt getting students to come up with the nth term, by first starting with 1-5, then jumping to 10, and 20 and then 100, where its not possible for students to just keep adding 2 to the next line.
and how we can question students until they understand why they do certain stuff.. its called socratic questionning… so we imitated our questions, and we asked each other questions and i finally understood..
you see, the difference (an increase of constant 2) each line is actually speed. why? because it denotes an increase in value 2 each second. which is speed. distance per second. and x happens to be the value of time. what do you get when you multiply speed and time? you get distance!
now, what does the 5 in y=mx+5 mean? that’s the starting point. in the graph, its the y-intercept right? for a displacement-time graph, that would be the starting point.
and y would be your final point.
the final point would be the starting point (5) plus the distance travelled (2: speed X x:time)….. which is equals to y!!!!!
im not sure how many ppl know abt this……. but for me…. its actually the first time i understood what y=mx+c means!!!! and basically it can represent anything! it could be rate of water leaving the tap… could be anything.. cos m represents rate of change. c is a constant…
ooooooo… ive learnt something new today! and when i finally understood it, i went, “so thats what it means!!!”