https://file.aiquickdraw.com/mathbot/file/1727800965356y52mgs38.jpg

Let's analyze the graph and the questions provided.

### Graph Information:
The graph shows calories burned (y-axis) versus the number of minutes (x-axis) Maria studied. The relationship is linear, meaning the number of calories burned is directly proportional to the number of minutes.

### Step 1: Calculate the slope of the graph
The slope represents how many calories Maria burns per minute.

To find the slope:
- Select two points from the graph. From the image, let's approximate two clear points:
  1. Point 1: \((0, 0)\) — no minutes, no calories burned.
  2. Point 2: \((60, 200)\) — after 60 minutes, Maria has burned 200 calories.

The formula for slope \(m\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute the points \((0, 0)\) and \((60, 200)\):
\[
m = \frac{200 - 0}{60 - 0} = \frac{200}{60} = \frac{10}{3} \approx 3.33
\]
So, the slope is approximately **3.33 calories per minute**.

### Step 2: Answer the questions
**(a) How many calories is Maria burning per minute?**
- Based on the slope calculation, Maria is burning **3.33 calories per minute**.

**(b) What is the slope of the graph?**
- The slope is **3.33**.

These are the correct answers based on the provided graph.

Would you like a more detailed explanation of the solution, or do you have any other questions?

### Relative Questions:
1. How do you find the equation of a line using the slope and a point?
2. What would happen to the slope if Maria burns calories at a faster rate?
3. How can you interpret the y-intercept in a real-world scenario like this one?
4. How does the concept of direct variation apply to this situation?
5. Can you explain how to estimate points on a graph accurately?

### Tip:
When interpreting linear graphs, always use the slope formula to check how changes in one variable (minutes) affect the other variable (calories burned).

This problem involves analyzing a linear graph where calories burned are directly proportional to the number of minutes studied. Learn how to calculate the slope (rate of calories burned per minute) using the formula m = (y2 - y1) / (x2 - x1). The solution is designed for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation