Question

a lake near the arctic circle is covered by a 2-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 3 weeks, the sheet is only 1.25 meters thick. let y represent the ice sheet’s thickness (in meters) after x weeks. which of the following information about the graph of the relationship is given? choose 1 answer: a slope and x-intercept b slope and y-intercept c slope and a point that is not an intercept d x-intercept and y-intercept e y-intercept and a point that is not an intercept f two points that are not intercepts

Explanation:

Step1: Determine the slope

The ice thickness starts at 2 meters (when \( x = 0 \), \( y = 2 \)) and after 3 weeks, it's 1.25 meters. The slope \( m \) is calculated as \( \frac{\Delta y}{\Delta x}=\frac{1.25 - 2}{3-0}=\frac{- 0.75}{3}=- 0.25 \). So we have the slope.

Step2: Determine the y - intercept

When \( x = 0 \) (at the start, before any weeks have passed), the ice thickness \( y = 2 \) meters. So the y - intercept is 2.
We have the slope ( - 0.25) and the y - intercept (2) for the linear relationship \( y=mx + b \) (where \( m \) is the slope and \( b \) is the y - intercept).

Answer:

B. Slope and y - intercept