. 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.

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.

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carlosego carlosego · Answer 2 · 2018-09-06T15:44:02+02:00

The generic equation of the line is:

[tex] H-H0 = m (T-T0) [/tex]

Where,

m: slope of the line

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

The slope of the line is:

[tex] m =\frac{H2-H1}{T2-T1} [/tex]

Substituting values we have:

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

Rewriting:

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

[tex] m = -1 [/tex]

Then, choosing an ordered pair we have:

[tex] (T0, H0) :( 5, 15) [/tex]

Substituting values we have:

[tex]H-15=-(T-5)[/tex]

Rewriting the equation:

[tex]H-15=-T+5[/tex]

[tex]H=-T+5+15[/tex]

[tex]H=-T+20[/tex]

Then, for 8 hours we have:

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

[tex]H=12[/tex]

Answer:

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

[tex]H=-T+20[/tex]

the candle will be 12 inches after burning 8 hours