A candle is 17 in. tall after burning for 3 hours. After 5 hours, it is 15 in. tall. Write a linear equation to model the relationship between heigh h of the candle and time t. Predict how tall the candle will be after 8 hours.

For the linear equation you have two points (3, 17) and (5, 15) so the equation is: h-17=(15-17)/(5-3)*(t-3), solve for h= -t+20.
For predicting, only replace t=8 into you equation (h= -t+20) and you will get h=-8+20=12

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calculista calculista · Answer 2 · 2018-10-09T11:07:06-04:00

Let

x------> the time in hours

y------> the height in inches

\(A(3,17)\\B(5,15)\)

Step \(1\)

Find the slope m of the linear equation between points A and B

we know that

The formula to calculate the slope between two points is equal to

\(m=\frac{(y2-y1)}{(x2-x1)}\)

substitutes the values

\(m=\frac{(15-17)}{(5-3)}\)

\(m=\frac{(-2)}{(2)}\)

\(m=-1\)

Step \(2\)

Find the equation of the line

we know that

the equation of the line in the point-slope form is

\(y-y1=m*(x-x1)\)

we have

\(m=-1\)

\(A(3,17)\)

substitute in the equation

\(y-17=-1*(x-3)\)

\(y=-x+20\) --------> this is the linear equation that model the relationship between height h of the candle and time t

Step \(3\)

Find the height for \(x=8\) hours

substitute the value of x in the linear equation

\(y=-8+20\)

\(y=12\ inches\)

The height of the candle will be \(12\ inches\) after \(8\ hours\)