Nevaeh just lit a new candle and then let it burn all the way down to nothing. Let LL represent the length of the candle remaining unburned, in inches, tt hours after candle was lit. The table below has select values showing the linear relationship between tt and L, .L. Determine the number of inches of candle that burns per hour.
tt	LL
3, point, 53.5	3, point, 2, 53.25
55	2, point, 52.5
88	11


The given problem involves a linear relationship between time \( t \) (hours) and the length \( L \) of the candle remaining (in inches).

From the table:

| \( t \) (hours) | \( L \) (inches) |
|-----------------|------------------|
| 3               | 3.5              |
| 5               | 3.25             |
| 8               | 2.5              |
| 11              | 1                |

Since the relationship is linear, we can calculate the rate at which the candle burns per hour (the slope) using any two points from the table. Let's use the points \( (3, 3.5) \) and \( (5, 3.25) \).

The formula for the slope \( m \) is:

\[
m = \frac{L_2 - L_1}{t_2 - t_1}
\]

Using the points \( (t_1 = 3, L_1 = 3.5) \) and \( (t_2 = 5, L_2 = 3.25) \):

\[
m = \frac{3.25 - 3.5}{5 - 3} = \frac{-0.25}{2} = -0.125
\]

Thus, the candle burns at a rate of **0.125 inches per hour**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would you determine the total time the candle will burn before it is completely gone?
2. What would the candle's length be after 10 hours of burning?
3. Can you determine the initial length of the candle using this data?
4. What is the equation of the line representing the relationship between time and candle length?
5. How would this problem change if the candle burned at a non-linear rate?

**Tip:** To find the slope of a linear relationship, always use two points from the data set and apply the slope formula.

Nevaeh just lit a new candle and then let it burn all the way down to nothing. Let L represent the length of the candle remaining unburned, in inches, t hours after the candle was lit. The table below has select values showing the linear relationship between t and L. Determine the number of inches of candle that burns per hour. t  |  L (inches)  3  |  3.5  5  |  3.25  8  |  2.5  11 |  1

Learn how to determine the rate at which a candle burns using a linear relationship between time and length. The problem involves calculating the slope using the given data points (3, 3.5), (5, 3.25), (8, 2.5), and (11, 1), making it suitable for students in Grades 6-8.

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