Question

A candle is 8 inches tall after burning for 1 hour. After 3 hours it is 5.5 inches tall.
What is the equation in y=mx+b form to model the height "Y" of the candle at time "x" ??

Answer 1

Answer:

Step-by-step explanation:

Let x=time elapsed (in hours) and y=height of candle (in inches)  

Since the "candle is 8 inches tall after burning for 1 hour", this means that we have the values x=1 and y=8 which is the point (1,8)  

Also, the statement "After 3 hours it is 5.5 inches tall" tells us that x=3 and y=5.5 which forms the point (3,5.5)  

Now let's find the equation of the line through the points (1,8) and (3,5)  

First let's find the slope of the line through the points  and  

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.  

m=%285.5-8%29%2F%283-1%29 Plug in y%5B2%5D=5.5, y%5B1%5D=8, x%5B2%5D=3, and x%5B1%5D=1  

m=%28-2.5%29%2F%283-1%29 Subtract 8 from 5.5 to get -2.5  

m=%28-2.5%29%2F%282%29 Subtract 1 from 3 to get 2  

m=-1.25 Divide  

So the slope of the line that goes through the points  and  is m=-1.25  

Now let's use the point slope formula:  

 

y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula  

y-8=-1.25%28x-1%29 Plug in m=-1.25, x%5B1%5D=1, and y%5B1%5D=8  

y-8=-1.25x%2B%28-1.25%29%28-1%29 Distribute  

y-8=-1.25x%2B1.25 Multiply  

y=-1.25x%2B1.25%2B8 Add 8 to both sides.  

y=-1.25x%2B9.25 Combine like terms.  

So the equation that goes through the points  and  is y=-1.25x%2B9.25  

Notice how the graph of y=-1.25x%2B9.25 goes through the points  and . So this visually verifies our answer.  

Graph of y=-1.25x%2B9.25 through the points  and  

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Answer:  

So the equation that models the height "y" at time "x" is  

y=-1.25x%2B9.25