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 · 2018-10-09T17:07:06+02:00

Let

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

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

[tex]A(3,17)\\B(5,15)[/tex]

Step [tex]1[/tex]

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

[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]

substitutes the values

[tex]m=\frac{(15-17)}{(5-3)}[/tex]

[tex]m=\frac{(-2)}{(2)}[/tex]

[tex]m=-1[/tex]

Step [tex]2[/tex]

Find the equation of the line

we know that

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

[tex]y-y1=m*(x-x1)[/tex]

we have

[tex]m=-1[/tex]

[tex]A(3,17)[/tex]

substitute in the equation

[tex]y-17=-1*(x-3)[/tex]

[tex]y=-x+20[/tex] --------> this is the linear equation that model the relationship between height h of the candle and time t

Step [tex]3[/tex]

Find the height for [tex]x=8[/tex] hours

substitute the value of x in the linear equation

[tex]y=-8+20[/tex]

[tex]y=12\ inches[/tex]

The height of the candle will be [tex]12\ inches[/tex] after [tex]8\ hours[/tex]