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?

The height of the candle after 9 hours can be written as 23.4 cm.

The linear relationship is the relationship between two variables such that it follows a straight line.

As it is given that the height of the candle is linear to the amount of time. Now, let's the time be on the x-axis and the y-axis be the height of the candle. therefore, the slope of the linear relationship can be represented as,

Point1 of the slope, (x₁, y₁) = (6, 24.6)

Point2 of the slope, (x₂, y₂) = (21, 18.6)

Now, since we know the two points of the linear relationship, therefore, the slope can be written as,

Thus, the slope of the linear relationship is -0.4.

Now, the equation of the linear relationship can be written as,

Thus, the Linear relationship of the candle height and the amount of time can be written as .

Now, In order to calculate the height of the candle after 9 hours, we will substitute the value of the x as 9.

Hence, the height of the candle after 9 hours can be written as 23.4 cm.

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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

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

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.

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