Question

practice:
y
battery life percentage
0 2 4 6 8 10
hours after 7 am

1. interpret the slope
2. interpret the y - intercept:

Explanation:

Step1: Identify Slope Formula

The slope \( m \) of a line is calculated as \( m=\frac{y_2 - y_1}{x_2 - x_1} \). From the graph, we can take two points on the line, e.g., \( (0, 80) \) (y - intercept) and \( (10, 20) \).

Step2: Calculate Slope

Substitute \( (x_1,y_1)=(0,80) \) and \( (x_2,y_2)=(10,20) \) into the slope formula:
\( m=\frac{20 - 80}{10 - 0}=\frac{- 60}{10}=- 6 \).

Step3: Interpret Slope

The slope represents the rate of change of battery life percentage with respect to hours after 7 AM. A slope of - 6 means the battery life percentage decreases by 6 percentage points per hour after 7 AM.

Step4: Interpret y - Intercept

The y - intercept is the value of \( y \) when \( x = 0 \). From the point \( (0,80) \), when \( x = 0 \) (0 hours after 7 AM, i.e., at 7 AM), the battery life percentage is 80%.

Answer:

• Slope Interpretation: The battery life percentage decreases by 6 percentage points per hour after 7 AM.
• y - Intercept Interpretation: At 7 AM (0 hours after 7 AM), the battery life percentage is 80%.