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

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:

$m =\frac{H2-H1}{T2-T1}$

Substituting values we have:

$m =\frac{15-17}{5-3}$

Rewriting:

$m =\frac{-2}{2}$

$m = -1$

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

Answer 2

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.