Use the situation below to answer all parts of question 3.

Question

A lake near the Arctic Circle is covered by a 3-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 by 0.75 meters each week.

Part 1

Identify the equation that represents this situation.

Responses

y = 0.75x + 3
y = 0.75x + 3

y = -0.75x + 3
y = -0.75x + 3

y = 3x + 0.75
y = 3x + 0.75

y = -3x + 0.75
y = -3x + 0.75
Question 2
Part 2
The slope in this situation is
Choose...
and represents the
Choose...
.

The y-intercept in this situation is
Choose...
and represents the
Choose...
.

Answer 1

Part 1

The best equation that represents the situation described is:

y = -0.75x + 3

This is because the ice thickness decreases over time, so the slope should be negative (indicating a decrease). The initial thickness of the ice was 3 meters, which is represented by the y-intercept.

Part 2

The slope in this situation is -0.75 and represents the decrease in ice thickness (in meters) per week.

The y-intercept in this situation is 3 and represents the initial thickness of the ice (3 meters) at the beginning of spring (when x = 0).