Question

Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 6 hours of burning, a candle has a height of 24.6 centimeters. After 21 hours of burning, its height is 18.6 centimeters. What is the height of the candle after 9 hours?

Answer 1

Given: After 6 hours of burning, a candle has a height of 24.6 centimeters. After 21 hours of burning, its height is 18.6 centimeters.

Solution: We could write coordinates for number of hours and height of the candle (hours, height) for the above data as

(6,24.6) and (21,18.6).

In order to find the linear function, we need to find the slope between those two coordinates.

Slope would represent the rate at which length of candle is decreasing.

Let is find slope between those two coordinates now.

We know, slope formula

$m= \frac{y2-y1}{x2-x1}$

We have (x1,y1)=(6,24.6)  and (x2,y2) = (21,18.6).

Plugging values of x1,y1,x2 and y2 in slope formula, we get

$m=\frac{18.6-24.6}{21-6}=\frac{-6}{15}$

Simplfying fraction -6/15 into simplest form, we get

-2/5.

So, the slope m=-2/5.

In decimal form -2/5 = -0.4.

Applying point-slope form of the linear equation

y-y1 = m(x-x1)

y- 24.6= -0.4(x-6).

Distributing -0.4 over (x-6), we get -0.4*x -0.4*-6 = -0.4x +2.4

y-24.6 = -0.4x +2.4

Adding 24.6 on both sides, we get

y-24.6+24.6 = -0.4x +2.4+24.6

y = -0.4x + 27.

Now, we need to find height of the candle after 9 hours.

x represents number of hours there.

Plugging x=9 in above function we got,

y = -0.4(9) + 27

y= -3.6 +27

y =23.4

Therefore, 23.4 centimeters is the height of the candle after 9 hours.