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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

object A
object A

all of the objects
all of the objects

object C

1 answer

To determine which object is moving at a rate of 2 feet per second, we need to analyze the slopes of the lines corresponding to each object.

  1. Object A: The line passes through points (0, 0) and (3, 6).

    • Slope = (Change in y) / (Change in x) = (6 - 0) / (3 - 0) = 6/3 = 2 feet per second.

  2. Object B: The line passes through points (0, 0) and (6, 6).

    • Slope = (Change in y) / (Change in x) = (6 - 0) / (6 - 0) = 6/6 = 1 foot per second.

  3. Object C: The line passes through points (0, 0) and (6, 3).

    • Slope = (Change in y) / (Change in x) = (3 - 0) / (6 - 0) = 3/6 = 0.5 feet per second.

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

So, the answer is: object A.