Use the image to answer the question.

Question

An illustration shows quadrant one of a coordinate plane where the x-axis and y-axis range from 0 to 6 in increments of 1. The y-axis is titled distance in feet and the x-axis is titled time in seconds. A solid line, labeled A, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 3 comma 6 right parenthesis. A dotted line, labeled B, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 6 right parenthesis. A dashed line, labeled C, is marked on the graph and passes through coordinates left parenthesis 0 comma 0 right parenthesis and left parenthesis 6 comma 3 right parenthesis.

Which of these objects is moving at a rate of 2 feet per second?

(1 point)
Responses

object B
object B

object A
object A

all of the objects
all of the objects

object C
object C
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Answer 1

To determine which object is moving at a rate of 2 feet per second, we need to find the slope of each line since the slope represents the rate of change in distance with respect to time (distance/time = rate).

1. Object A:

   • Coordinates: (0, 0) to (3, 6)
   • Slope = (Change in y) / (Change in x) = (6 - 0) / (3 - 0) = 6 / 3 = 2 feet/second.

2. Object B:

   • Coordinates: (0, 0) to (6, 6)
   • Slope = (6 - 0) / (6 - 0) = 6 / 6 = 1 foot/second.

3. Object C:

   • Coordinates: (0, 0) to (6, 3)
   • Slope = (3 - 0) / (6 - 0) = 3 / 6 = 0.5 feet/second.

Based on the above calculations, object A is the only object moving at a rate of 2 feet per second.

So the answer is:

object A