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The image contains text that needs to be solved. I'll extract the mathematical content from the image and provide a solution.

### Extracted Problem:
> The fuel level in a car is shown. For the fuel to be 50 mm deep, there is 5 L, and the car is supposed to have 15 L of fuel in it. Taking the distance covered by the level of fuel left as \( x \), write a linear equation for the fuel level and find the three possible solutions. What is the fuel level for 10 L and 13 L?

### Solution:

We need to write a linear equation relating the fuel level depth (in mm) to the volume of fuel (in liters).

#### Step 1: Identify Points to Form the Linear Equation
- When the fuel depth is 50 mm, the fuel volume is 5 L.
- The car is supposed to have 15 L, but the corresponding depth is not given directly.

Let's assume a linear relationship of the form:

\[
y = mx + c
\]

where:
- \(y\) is the fuel level in mm,
- \(x\) is the volume of fuel in liters,
- \(m\) is the slope,
- \(c\) is the y-intercept.

#### Step 2: Find the Slope \(m\)
We need another point to determine the slope. Let's assume the fuel tank is empty at 0 mm depth and 0 L.

- Two points: \((0, 0)\) and \((5, 50)\).

The slope \(m\) is calculated as:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{50 - 0}{5 - 0} = 10 \, \text{mm/L}
\]

#### Step 3: Write the Linear Equation
Since the line passes through the origin (0,0), the y-intercept \(c = 0\). Thus, the equation is:

\[
y = 10x
\]

#### Step 4: Solve for 10 L and 13 L
1. For 10 L:
   \[
   y = 10 \times 10 = 100 \, \text{mm}
   \]

2. For 13 L:
   \[
   y = 10 \times 13 = 130 \, \text{mm}
   \]

### Conclusion
- The linear equation for the fuel level is \(y = 10x\).
- The fuel level for 10 L is 100 mm.
- The fuel level for 13 L is 130 mm.

Would you like more details, or do you have any questions?

### Related Questions
1. How do you determine the slope of a line given two points?
2. What is the significance of the y-intercept in a linear equation?
3. How can this linear model be used to predict other fuel levels?
4. What assumptions are we making about the shape of the fuel tank?
5. How would the equation change if the tank depth was not proportional to the volume?

### Tip
Remember, the slope \(m\) in a linear equation represents the rate of change between two variables.

The fuel level in a car is shown. For the fuel to be 50 mm deep, there is 5 L, and the car is supposed to have 15 L of fuel in it. Taking the distance covered by the level of fuel left as x, write a linear equation for the fuel level and find the three possible solutions. What is the fuel level for 10 L and 13 L?

Learn how to solve a real-world problem by writing a linear equation for the fuel level in a car. This problem explores the relationship between the fuel depth and volume, and solves for specific fuel levels at 10L and 13L. Suitable for students in Grades 9-11.

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