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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

all of the objects
all of the objects

object C
object C

object A
object A
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1 answer

To determine which object is moving at a rate of 2 feet per second, we can analyze the slopes of the lines represented by each object.

  1. Object A has points (0, 0) and (3, 6):

    • The change in distance (y) = 6 - 0 = 6 feet
    • The change in time (x) = 3 - 0 = 3 seconds
    • Rate = change in distance / change in time = 6 feet / 3 seconds = 2 feet per second.

  2. Object B has points (0, 0) and (6, 6):

    • The change in distance (y) = 6 - 0 = 6 feet
    • The change in time (x) = 6 - 0 = 6 seconds
    • Rate = change in distance / change in time = 6 feet / 6 seconds = 1 foot per second.

  3. Object C has points (0, 0) and (6, 3):

    • The change in distance (y) = 3 - 0 = 3 feet
    • The change in time (x) = 6 - 0 = 6 seconds
    • Rate = change in distance / change in time = 3 feet / 6 seconds = 0.5 feet per second.

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