Question

A lake near the Arctic ˚le is covered by a 222-meter-thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After 333 weeks, the sheet is only 1.25 meters thick. Let yyy represent the ice sheet's thickness (in meters) after xxx weeks. Which of the following information about the graph of the relationship is given?

a) Slope and xxx-intercept
b) Slope and yyy-intercept
c) Slope and a point that is not an intercept
d) xxx-intercept and yyy-intercept

Answer 1

The graph of the relationship between ice sheet thickness and time has a given y-intercept (222 meters) and a calculable slope, which is the rate of decrease in thickness per week.

Step-by-step explanation:

The question asks which information about the graph of the relationship between the ice sheet's thickness (represented by y) after x weeks is given, based on the scenario where a 222-meter-thick ice sheet reduces to 1.25 meters after 333 weeks. Since we know the initial thickness (222 meters) when x=0, and the thickness after a certain time (1.25 meters at x=333 weeks), we can determine the y-intercept (222 meters) and the slope of the graph (change in thickness per week). The slope can be calculated by the change in ice thickness divided by the number of weeks. The rate of decrease in thickness is constant, and the graph would be a straight line, indicating that the option containing both 'slope' and 'y-intercept' is correct.

To calculate the slope:

Slope = (Change in thickness) / (Change in time) = (1.25 - 222) / (333 - 0) = -220.75 / 333