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The graph shows the percentage of battery \( B \) remaining as a function of time \( t \), measured in hours since Robert left his house. From the graph, we can observe that the relationship between \( B \) and \( t \) is linear.

To find the equation for \( B \), we need to determine the slope and y-intercept of the line. The equation of a line is generally written as:

\[
B = mt + b
\]

where \( m \) is the slope and \( b \) is the y-intercept (the value of \( B \) when \( t = 0 \)).

### Step 1: Identify two points on the graph
From the image, two clearly defined points on the line are:
- \( (0, 32) \) (when Robert left his house, the battery was at 32%)
- \( (6, 0) \) (after 6 hours, the battery was at 0%)

### Step 2: Calculate the slope \( m \)
The slope is given by the formula:

\[
m = \frac{\text{change in } B}{\text{change in } t} = \frac{B_2 - B_1}{t_2 - t_1}
\]

Using the points \( (0, 32) \) and \( (6, 0) \):

\[
m = \frac{0 - 32}{6 - 0} = \frac{-32}{6} = -\frac{16}{3}
\]

### Step 3: Write the equation
Now that we have the slope \( m = -\frac{16}{3} \), and we know the y-intercept is 32 (since \( B = 32 \) when \( t = 0 \)), the equation for \( B \) is:

\[
B = -\frac{16}{3}t + 32
\]

### Step 4: Find the x-intercept
The x-intercept is the value of \( t \) when \( B = 0 \). To find it, we set \( B = 0 \) in the equation and solve for \( t \):

\[
0 = -\frac{16}{3}t + 32
\]
\[
\frac{16}{3}t = 32
\]
\[
t = \frac{32 \times 3}{16} = 6
\]

### Interpretation of the x-intercept
The x-intercept represents the time when Robert's phone battery is completely drained. In this case, the x-intercept is 6, meaning that after 6 hours, Robert's phone battery reaches 0%.

### Summary:
- Equation for \( B \): \( B = -\frac{16}{3}t + 32 \)
- x-intercept: \( t = 6 \) (After 6 hours, the battery is fully drained)

Would you like further details or have any questions? Here are some related questions:

1. What is the meaning of the slope in this context?
2. How would the equation change if Robert started with a different initial charge?
3. What would happen to the x-intercept if the phone drained faster?
4. How can you predict the battery level after 4 hours using the equation?
5. What is the rate of battery depletion per hour according to this model?

**Tip**: When interpreting graphs, always check both the x-intercept and y-intercept for important real-world meanings.

Let B represent the charge remaining in Robert's battery, as a percentage, t hours since Robert left his house. Write an equation for B then state the x-intercept of the graph and determine its interpretation in the context of the problem.

Learn how to write a linear equation for battery charge as a function of time. The solution involves calculating the slope using two points on the graph, determining the equation, and interpreting the x-intercept in real-world terms. Suitable for Grades 9-10 students.

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