Use the image to answer the 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 C
object C
all of the objects
all of the objects
object A
object A
object B
object B
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The object that is moving at a rate of 2 feet per second is object A.
To determine which object is moving at a rate of 2 feet per second, we need to examine the slope of the lines on the graph. The slope represents the rate of change, which in this case is the rate of change in distance per unit of time.
Let's analyze each object:
Object A:
The line A passes through the points (0,0) and (3,6). To find the slope, we can use the formula: slope = (change in y) / (change in x).
(change in y) = 6 - 0 = 6
(change in x) = 3 - 0 = 3
slope of A = 6/3 = 2
Object B:
The line B passes through the points (0,0) and (6,6). Again, using the slope formula:
(change in y) = 6 - 0 = 6
(change in x) = 6 - 0 = 6
slope of B = 6/6 = 1
Object C:
The line C passes through the points (0,0) and (6,3). Using the slope formula yet again:
(change in y) = 3 - 0 = 3
(change in x) = 6 - 0 = 6
slope of C = 3/6 = 0.5
From the analysis above, we can see that only Object A has a slope of 2. Thus, the object moving at a rate of 2 feet per second is object A.