Einstein

media type="custom" key="6252649" Slope Formula:

Slope is the ratio of the vertical change to the horizontal change. It measures the steepness of the line.
Example: (1,-4) and (-4,2). . . . . . . . . . . . . . . . . . . . . . Example 3: m= [2-(-4)] / (-4-1). . . . . . . . . . . . . . . . . . . . (-5, 2) and (4, -7) m= (2+4) / (-5). . . . . . . . . . . . . . . . . . . . . . m= (-7-2) / [4-(-5)] m= 6 / -5. . . . . . . . . . . . . . . . . . . . . . . . . . m= -9 / (4+5) m= -(6/5). . . . . . . . . . . . . . . . . . . . . . . . . . m= -9 / 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m= -1

Example 2: ................................................ Example 4: (1,1) and (5,1) ............................................ (3,4) and (3,6) m= (1-1) / (5-1) ........................................... m= (6-4) / (3-3) m= 0 / 4 .................................................... m= 2 / 0 m= 0 ......................................................... m= undefined

The slope can be used in the point slope equation [y-y1=m(x-x1)] and the slope intercept equation (y=mx+b).

​__ **rise** __- how many units you move up or down from point to point (change in y value) __ **run** __- how far left to right you move from point to point (change in x value) __ **positive slope** __- goes up left to right __ **negative slope** __ - goes down left to right __ **zero slope** __- horizontal __ **undefined slope** __- vertical
 * __Slope:__ ** rise over run

__ Word Problem: __ One month your long distance bill was $31 and you talked for 600 minutes. The next month you talked 750 minutes and your bill was $37. a) determine the linear function that describes this relation b) what is the slope of your function? c) what is the real meaning of the slope? d) what is the y-intercept of your function? e) what is the real meaning of the y- intercept? f) how much would you expect to pay if you talked for 350 minutes? g) if your bill was $40, how many minutes did you use?

a) let x= cost let y= minutes

First month: (31, 600) Second month: (37, 750)

m = (y2 - y1) / (x2 - x1) m = 600-750 / 31-37 m = -150 / -6 m = 25

The slope is 25

y = 25x + b. 600 = 25(31) + b 600 = 775 + b 600-775 = 775-775 + b -175 = b b) The slope is 25

c) The slope is the value by which the price rises (you know that it's rising and not falling because the slope is positive)

e) The real meaning of the y-intercept is the cost at which you started with

f) 350 = 25x - 175 350 + 175 = 25x -175 + 175 350 + 175 = 25x 525 = 25x 525 / 25 = 25x / 25 21 = x

You would expect to pay $21

g) y = 25x - 175 y = 25(40) - 175 y = 1000 - 175 y = 825

You used 825 minutes