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put this solution on YOUR website!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
)
Start with the slope formula.
Plug in
,
,
, and
Subtract
from
to get
Subtract
from
to get
Divide
So the slope of the line that goes through the points
and
)
is
Now let's use the point slope formula:
Start with the point slope formula
Plug in
,
, and
Distribute
Multiply
Add 8 to both sides.
Combine like terms.
So the equation that goes through the points
and
is
Notice how the graph of
goes through the points
and
. So this visually verifies our answer.
Graph of
through the points
and
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Answer:
So the equation that models the height "y" at time "x" is
(