Question

Ayesha sails her boat in a straight line away from the dock at a constant speed. After 20 minutes, she has traveled 4 kilometers. If Ayesha’s trip is graphed as a function on a coordinate plane where x represents time in hours and y represents her distance from the dock in kilometers, what is the slope of the line?

a) 0.2
b) 0.333
c) 1
d) 5

Answer 1

The slope of the line on the coordinate plane, which represents Ayesha's distance over time, is 0.2 km/minute. This is option a) 0.2, as it is the rate of distance covered per minute when the 20-minute travel time is converted to hours and then to minutes.

Step-by-step explanation:

To find the slope of the line representing Ayesha's boating trip on a coordinate plane where x represents time in hours and y represents her distance from the dock in kilometers, we can use the formula for calculating the slope (slope = rise/run), which in this case translates to the distance traveled divided by the time taken. Since Ayesha traveled 4 kilometers in 20 minutes, we must first convert 20 minutes to hours, which is 20 minutes / 60 minutes/hour = 0.333 hours. The slope is therefore 4 km / 0.333 hours = 12 km/hour.

However, the answer choices provided in the question seem to indicate the expectation of the speed in kilometers per minute, thus we need to find the corresponding rate. 12 km/hour divided by 60 minutes/hour gives 0.2 km/minute. Therefore, the correct answer amongst the options given is a) 0.2.