Question

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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 50 and 4 comma 0.

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)

Answer 1

The equation in slope-intercept form is y = -25x + 100. The slope represents the rate of change of the percent of battery remaining concerning the number of hours. The slope of -25 means that for every increase of 1 hour, the percent of battery remaining decreases by 25.

Step-by-step explanation:

Part A: To write the equation in slope-intercept form, we need to find the slope (m) and the y-intercept (b). The slope is calculated as the change in y divided by the change in x, which can be found using the points (0, 100) and (2, 50). The change in y is 50 - 100 = -50 and the change in x is 2 - 0 = 2. Therefore, the slope (m) is -50/2 = -25. The y-intercept (b) can be found by plugging in the coordinates (0, 100) into the equation y = mx + b. Since y = 100 when x = 0, we can solve for b: 100 = (-25)(0) + b, which simplifies to b = 100. The equation in slope-intercept form is y = -25x + 100.

Part B: The equation was determined by finding the slope (m) and y-intercept (b) using the given points on the graph. The slope represents the rate of change of the y variable (percent of battery remaining) concerning the x variable (number of hours). In this case, the slope of -25 means that for every increase of 1 hour, the percent of battery remaining decreases by 25.

Part C: The slope in the given situation represents the rate of change of the percent of battery remaining concerning the number of hours. In this case, the slope of -25 means that for every increase of 1 hour, the percent of battery remaining decreases by 25. This indicates that the battery is draining at a constant rate over time.