Question

. Could someone please explain this to me in detail. I am very confused. Thank you so much!. . A candle is 17 inches tall after burning for 3 hours. after 5 hours it is 15 inches tall. Write a linear equation to model the relationship between height H of the candle, and T time. predict how tall the candle will be after burning 8 hours.

Answer 1

We can translate the given data into points (hrs,inches). Hence, we have points (3,17) and (5,15). The rate at which the candle shortens is (15-17)/(5-3) equal to 1 inch per hour. Substituting this slope to the equation (y2-y1)= m(x2-x1) we have y-17= -1*(x-3) or y = -x + 20 where y is the length of the candle and x is the hours.

Answer 2

The generic equation of the line is:

`H-H0 = m (T-T0)`

Where,

m: slope of the line

(T0, H0): ordered pair belonging to the line.

The slope of the line is:

`m =(H2-H1)/(T2-T1)`

Substituting values we have:

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

Rewriting:

`m =(-2)/(2)`

`m = -1`

Then, choosing an ordered pair we have:

`(T0, H0) :( 5, 15)`

Substituting values we have:

`H-15=-(T-5)`

Rewriting the equation:

`H-15=-T+5`

`H=-T+5+15`

`H=-T+20`

Then, for 8 hours we have:

`H=-8+20`

`H=12`

Answer:

a linear equation to model the relationship between height H of the candle, and T time is:

`H=-T+20`

the candle will be 12 inches after burning 8 hours