Question 23664: how do i find the slope of the lines passing through the given points? Also how do i find the value of u so that the line passing thourgh the two points has a given slope? Also, how do i find the rate of change between the two points?
Answer by queenofit(120)   (Show Source):
You can put this solution on YOUR website! first, to find the slope of a line passing through two given points it helps to memorize the definition of the slope of a line
the slope "m" of the nonvertical line passing through the points (x1,y1) and (x2,y2) is
y2-y1 change in y
m= ----- = ------------
x2-x1 change in x
in other words if you had the points (1,0)and (0,2) plug them into the above formula for the slope. the first set is x1 and y1 and the second set is x2 and y2, get it? so you would have
2-0
--- = m (slope) 2/-1=-2 your slope would be -2 in this example.
0-1
for your second section of your question, I wasn't exactly sure of what you were asking. if you will email me an example I will be glad to help you with it. however, i think a point slope formula would work for you there.
as for your last question. this can be quite confusing. not because it is difficult, but because there are certain rules you must follow. you need to review the section in your textbook on direct variation for the rules. there will be an example for each I am sure, but I think you are asking about the following and since they mostly pertain to word problems that can be quite wordy, I will only do one example here, but I am willing to help out by email if you need more help. ok? so lets try to find the rate of change between two points when we know that our y intercept is a non Zero. we will have the formula y=mx+b. I assume you know this formula, if not please let me know by email and I will explain further.
you know that m represents the slope of the line. In real life problems the slpe can often be interpreted as the rate of change of y with respect to x. So lets do a word problem.
A mountain climber is climbing up a 500 foot cliff. By 1pm, the climber has climbed 115 feet up the cliff. by 4 pm the climber has reached a height of 280 feet
a. find the average rate fo change fo the climber and use this rate of change to find the equation that relates the height of the climber to the time.
let y represent the height of the climber and let t represent the time. Them the two points that represent the climber's two positions are
(t1,y1)=(1,115) and (t2,y2)= (4,280)
so, the average rate of change of the climber is
y2-y1
-----
t2-t1
280-115
-------
4-1
= 55 feet per hour
an equation that relates the height of the climber to the time is
y-y1=m(t-t1) point slope form
y-115=55(t-1) substitute y1=115, t1=1, and m=55
y=55t+60
hope this helps
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