https://file.aiquickdraw.com/mathbot/file/1721805819805zzrnidub.jpeg

To solve the problem of how many hours it will take for Iliana to get 200 total XP based on the given graph, we need to analyze the relationship between the playing time (\(t\)) and the total XP (\(p\)).

### Step-by-Step Solution:

1. **Extract Data Points from the Graph**:
   The graph shows the total XP (\(p\)) on the vertical axis and the playing time (\(t\)) on the horizontal axis. From the graph, we can see the following data points:
   - At \( t = 1 \) hour, \( p \approx 20 \)
   - At \( t = 2 \) hours, \( p \approx 30 \)
   - At \( t = 3 \) hours, \( p \approx 40 \)
   - At \( t = 4 \) hours, \( p \approx 50 \)
   - At \( t = 5 \) hours, \( p \approx 60 \)
   - At \( t = 6 \) hours, \( p \approx 70 \)

2. **Determine the Relationship**:
   The data points suggest a linear relationship between \(t\) and \(p\). Let's calculate the slope \(m\) of the line using two points (e.g., \( (1, 20) \) and \( (6, 70) \)):
   \[
   m = \frac{p_2 - p_1}{t_2 - t_1} = \frac{70 - 20}{6 - 1} = \frac{50}{5} = 10
   \]
   Thus, the slope \(m = 10\).

3. **Formulate the Equation**:
   Using the slope-intercept form of a linear equation \( p = mt + b \), and one of the points, say \( (1, 20) \):
   \[
   20 = 10 \cdot 1 + b \implies b = 10
   \]
   Therefore, the linear equation relating \(t\) and \(p\) is:
   \[
   p = 10t + 10
   \]

4. **Solve for \(t\) when \(p = 200\)**:
   \[
   200 = 10t + 10 \implies 200 - 10 = 10t \implies 190 = 10t \implies t = \frac{190}{10} = 19
   \]

### Answer:
Iliana will need to play for 19 hours to get 200 total XP.

Would you like any more details or have any questions? Here are some additional questions you might be interested in:

1. How do we determine if a relationship is linear or nonlinear?
2. Can you explain the slope-intercept form of a linear equation?
3. How can we verify the accuracy of our linear model?
4. What are the different types of relationships between variables?
5. How do we interpret the slope and intercept in the context of this problem?

**Tip:** Always check the data points to ensure they fit well with the linear model before making predictions based on the model.

Explore how to calculate the playing time required to achieve 200 XP through a detailed analysis of a linear relationship. Learn about the slope-intercept form of a linear equation and its application in solving real-world problems. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation