Question 119295: In the algebraic slope formula; y=mx+b why is "m" used to identify the slope and "b" the y-intercept?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Sorry; I misread your question.
---------------
The slope tells you how much y changes when x changes one.
Assume you have f(x) = mx +b
When x increases by one you get:
f(x+1) = m(x+1)+b
f(x+1) = mx + m + b
-------
So, how much did y cange when x changed by one?
Subtract to find out, as follows:
f(x+1)-f(x) = mx+m+b - (mx+b) = m
----------
The y value increased by "m" when the x value increased by one,
so "m" is the slope.
=========================
The y-intercept tells you where the graph would cross the y-axis.
The y-axis is the line where x = 0
So, if you have f(x) = mx+b
Then f(0) = m*0 + b = b
Therefore b is the y-intercept.
====================
Cheers,
Stan H.
|
|
|
