# Step-by-Step Solution ## **Understanding the Graph** - **Title**: Constant Force; m(x) over a(y) - **X-axis**: Mass (m) - **Y-axis**: Acceleration (a) - **Data Points**: - (50, 4) - (100, 2) - (150, 1.3) - (200, 1) - (250, .8) ## **Step 1: Recall Newton's Second Law** Newton's Second Law states: \[ F = m \cdot a \] If the force \( F \) is constant, then: \[ a = \frac{F}{m} \] This means **acceleration is inversely proportional to mass**. --- ## **Step 2: Verify Inverse Relationship** Check if \( m \cdot a \) is (approximately) constant: - For (50, 4): \( 50 \times 4 = 200 \) - For (100, 2): \( 100 \times 2 = 200 \) - For (150, 1.3): \( 150 \times 1.3 = 195 \) - For (200, 1): \( 200 \times 1 = 200 \) - For (250, .8): \( 250 \times .8 = 200 \) All values are approximately **200**. --- ## **Step 3: Interpret the Result** This confirms that the **force \( F \) is constant and equal to 200 (units not specified)**. --- ## **Step 4: Write Final Answer** ### **Final Answer** > **The graph demonstrates that when a constant force is applied, acceleration is inversely proportional to mass. The product \( m \times a \) is constant and equal to 200. Thus, the constant force applied is \( F = 200 \) (in the units used for mass and acceleration in the graph).** --- ### **Summary Table** | Mass (m) | Acceleration (a) | \( m \times a \) | |----------|------------------|------------------| | 50 | 4 | 200 | | 100 | 2 | 200 | | 150 | 1.3 | 195 | | 200 | 1 | 200 | | 250 | .8 | 200 | --- **If you have further questions or want to calculate acceleration or mass for different values, let me know!**

# Slope of the Graph ## **Understanding the Slope** The slope of the graph represents the relationship between mass \( m \) and acceleration \( a \). Since the graph shows the relationship \( a \) vs. \( m \), we will calculate the slope based on the data points provided. ## **Step 1: Identify Two Points** Choose two points from the graph for calculation: 1. Point A: (100, 2) 2. Point B: (200, 1) ## **Step 2: Calculate the Slope** The slope \( m \) of a line through two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \] Applying the coordinates from Point A and Point B: \[ \text{slope} = \frac{1 - 2}{200 - 100} = \frac{-1}{100} = -0.01 \] ## **Step 3: Interpret the Slope** The negative slope indicates that as mass increases, acceleration decreases, which is consistent with the inverse relationship described by Newton's Second Law. ## **Final Answer** > **The slope of the graph is -0.01, indicating that acceleration decreases with increasing mass.**