SOLUTION: http://media261.acellus.com/Library/00001230_92_731_A1.png copy and paste that to see the graph. Can someone help me?

Algebra ->  College  -> Linear Algebra -> SOLUTION: http://media261.acellus.com/Library/00001230_92_731_A1.png copy and paste that to see the graph. Can someone help me?      Log On


   

Question 1001492: http://media261.acellus.com/Library/00001230_92_731_A1.png
copy and paste that to see the graph.
Can someone help me?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
highlighted points:
(2000,1000)
(2012,3400)
the equation of a line that passes through these points is:
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (2000,1000) and (2012,3400)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (2000,1000) and (x%5B2%5D,y%5B2%5D) is the second point (2012,3400))


m=%283400-1000%29%2F%282012-2000%29 Plug in y%5B2%5D=3400,y%5B1%5D=1000,x%5B2%5D=2012,x%5B1%5D=2000 (these are the coordinates of given points)


m=+2400%2F12 Subtract the terms in the numerator 3400-1000 to get 2400. Subtract the terms in the denominator 2012-2000 to get 12




m=200 Reduce



So the slope is

m=200





------------------------------------------------


Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and (x%5B1%5D,y%5B1%5D) is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


y-1000=%28200%29%28x-2000%29 Plug in m=200, x%5B1%5D=2000, and y%5B1%5D=1000 (these values are given)



y-1000=200x%2B%28200%29%28-2000%29 Distribute 200


y-1000=200x-400000 Multiply 200 and -2000 to get -400000%2F1. Now reduce -400000%2F1 to get -400000

y=200x-400000%2B1000 Add 1000 to both sides to isolate y


y=200x-399000 Combine like terms -400000 and 1000 to get -399000

------------------------------------------------------------------------------------------------------------

Answer:



So the equation of the line which goes through the points (2000,1000) and (2012,3400) is:y=200x-399000


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=200 and the y-intercept is b=-399000


Notice if we graph the equation y=200x-399000 and plot the points (2000,1000) and (2012,3400), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=200x-399000 through the points (2000,1000) and (2012,3400)


Notice how the two points lie on the line. This graphically verifies our answer.




sorry for graph, it doesn't fit...these coordinates are away to big