SOLUTION: The graph shows data collected by measuring the height, h, in centimeters, of a burning candle at different times, t, in minutes. Which of the following equations best represents

Algebra ->  Equations -> SOLUTION: The graph shows data collected by measuring the height, h, in centimeters, of a burning candle at different times, t, in minutes. Which of the following equations best represents      Log On


   

Question 86094: The graph shows data collected by measuring the height, h, in
centimeters, of a burning candle at different times, t, in minutes.
Which of the following equations best represents the line drawn
through the data points?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I'm going to use x instead of t, and use y instead of h
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (0,10) and (20,0)


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 (0,10) and (x%5B2%5D,y%5B2%5D) is the second point (20,0))


m=%280-10%29%2F%2820-0%29 Plug in y%5B2%5D=0,y%5B1%5D=10,x%5B2%5D=20,x%5B1%5D=0 (these are the coordinates of given points)


m=+-10%2F20 Subtract the terms in the numerator 0-10 to get -10. Subtract the terms in the denominator 20-0 to get 20




m=-1%2F2 Reduce



So the slope is

m=-1%2F2





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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-10=%28-1%2F2%29%28x-0%29 Plug in m=-1%2F2, x%5B1%5D=0, and y%5B1%5D=10 (these values are given)



y-10=%28-1%2F2%29x%2B%28-1%2F2%29%280%29 Distribute -1%2F2


y-10=%28-1%2F2%29x%2B0 Multiply -1%2F2 and 0 to get 0%2F2. Now reduce 0%2F2 to get 0

y=%28-1%2F2%29x%2B0%2B10 Add 10 to both sides to isolate y


y=%28-1%2F2%29x%2B10 Combine like terms 0 and 10 to get 10

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Answer:



So the equation of the line which goes through the points (0,10) and (20,0) is:y=%28-1%2F2%29x%2B10


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1%2F2 and the y-intercept is b=10


Notice if we graph the equation y=%28-1%2F2%29x%2B10 and plot the points (0,10) and (20,0), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-1%2F2%29x%2B10 through the points (0,10) and (20,0)


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





So the equation is y=%28-1%2F2%29x%2B10

which is equivalent to


h=%28-1%2F2%29t%2B10

So the answer is B)