Ask a New Question
Menu

The percentage of battery remaining after a certain number of hours after a cellphone is turned on can be represented by the graph shown.

Graph with x axis labeled number of hours and y axis labeled percent of battery remaining, with line that passes through the points 0 comma 100 and 2 comma 80 and 4 comma 60.

Part A: Write an equation in slope-intercept form to describe the relationship in the graph. (2 points)

Part B: Explain how you determined the equation. (1 point)

Part C: What is the meaning of the slope in the given situation? (1 point)

1 answer

Part A: To find the equation in slope-intercept form (y = mx + b), we first determine the slope (m) using the points given in the graph: (0, 100) and (2, 80).

  1. Calculate the slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{80 - 100}{2 - 0} = \frac{-20}{2} = -10 \]

  2. Now, we will use the slope and one of the points to find the y-intercept (b). Using the point (0, 100): \[ y = mx + b \Rightarrow 100 = -10(0) + b \Rightarrow b = 100 \]

  3. Now, we can write the equation: \[ y = -10x + 100 \] So the equation in slope-intercept form is: \[ \boxed{y = -10x + 100} \]

Part B: To determine the equation, I first identified two points on the line from the graph: (0, 100) and (2, 80). I calculated the slope between these points, which represents the change in battery percentage per hour. After finding the slope as -10, I used the y-intercept from the point (0, 100) to write the equation in slope-intercept form.

Part C: The slope of -10 indicates that for each hour that the cellphone is used, the battery percentage decreases by 10%. In other words, as time increases (x increases), the battery percentage (y) decreases at a constant rate of 10% per hour. This means the battery life diminishes steadily over time when the phone is in use.