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What is the L=
The x-intersept of the function is ()which represents

To address the problem, let's first analyze the graph and question.

The graph shows the relationship between **L**, the length of the candle remaining (in inches), and **t**, the number of hours since the candle was lit. The line in the graph shows a negative linear trend, which means as time increases, the length of the candle decreases.

### Step 1: Write the equation for **L**

We can identify two key points on the line to calculate the slope and write the equation. Based on the graph:
- At **t = 0**, the length of the candle **L = 10 inches** (y-intercept).
- At **t = 10 hours**, the length of the candle **L = 0 inches** (the candle burns down completely).

Using the points (0, 10) and (10, 0), we calculate the slope (**m**):

\[
m = \frac{L_2 - L_1}{t_2 - t_1} = \frac{0 - 10}{10 - 0} = \frac{-10}{10} = -1
\]

Thus, the slope of the line is **-1**. Now, using the point-slope form of the equation \(L = mt + b\), where \(m\) is the slope and \(b\) is the y-intercept (which is 10):

\[
L = -1t + 10
\]

This is the equation that represents the length of the candle remaining after \(t\) hours.

### Step 2: Determine the x-intercept

The x-intercept occurs when \(L = 0\), i.e., when the candle has burned completely. Using the equation \(L = -t + 10\), set \(L = 0\) and solve for \(t\):

\[
0 = -t + 10
\]

\[
t = 10
\]

### Interpretation of the x-intercept:
The x-intercept is \(t = 10\), which means that after 10 hours, the candle has burned down completely, and there is no remaining length.

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Would you like a detailed explanation of any part? Here are five related questions you might want to explore:

1. How is the slope of a line calculated in different situations?
2. What does the slope represent in this candle-burning problem?
3. How would the graph change if the candle burned faster or slower?
4. How can you check if two points are sufficient to determine a line?
5. What if the candle had a different initial length? How would that affect the equation?

**Tip:** Always use two clear points on a line to calculate the slope, which is key to forming the equation!

Harper 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 candle was lit. A graph of L is shown below. Write an equation for L then state the x-intercept of the graph and determine its interpretation in the context of the problem.

Explore how linear functions model real-life situations like candle burning. This example demonstrates calculating the rate of change and interpreting the x-intercept in the context of a candle's length over time.

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