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

Write the equation of the line containing the two points (3,17) and (5,15).

Note, (3,17) means after 3 hours, the candle is 17 inches high.

Answer 2

okay so, \[m=\frac{ 15-17 }{ 5-3 }\]
\[m=\frac{ -2 }{ 2 }\]
m=-1?

Answer 3

Correct, slope = -1. Now write the equation of the line whose slope is -1 and passes through any of those 2 points.

Answer 4

well?

Answer 5

I am trying to figure out how to write the equation of the line.

Answer 6

Need help?

Answer 7

yes please!

Answer 8

There are 2 ways..I will show one way.

Equation of a line, y = mx + b, where m = slope and b = y-intercept.

so we have y = -1x + b (since we know that the slope is -1).

Now pick any of the 2 points, say (3,17).
So substitute x = 3 and y = 17 into the equation above and solve for b.

So we have 17 = -1(3) + b
17 = -3 + b
b = 20

So our equation is y = -1x + 20 or y = -x + 20.

@Sky.Dance Do you understand this clearly?

Answer 9

Yes now i understand. So to figure out how much the candle would melt after 8 hours i would just substitute 8 and figure out the amount it melted! thank you so much!

Answer 10

One second...our equation is y = -x + 20

The question asked for an equation H in terms of t.

So our equation is H = -t + 20

(becuase our x stands for time, t, and our y was the height, H, of the candle).

Answer 11

So our equation is H = -t + 20.

Now that we have this equation, how tall will the candle be after burning 8 hours?

Answer 12

@Sky.Dance