Question

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.

Answer 1

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

Answer 2

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=((y2-y1))/((x2-x1))`

substitutes the values

`m=((15-17))/((5-3))`

`m=((-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`