Compare Proportions from Graphs & Equations Quick Check
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Question
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 A
object A
object C
object C
all of the objects
all of the objects
object B
object C
To determine which object is moving at a rate of 2 feet per second, we need to examine the slopes of the lines on the graph.
The slope of a line represents the rate of change in the y-coordinate (distance) relative to the x-coordinate (time). It is calculated by dividing the change in y by the change in x.
Let's calculate the slopes of the three lines:
For Object A:
The coordinates are (0, 0) and (3, 6).
Change in y = 6 - 0 = 6
Change in x = 3 - 0 = 3
Slope = change in y / change in x = 6 / 3 = 2 feet per second
For Object B:
The coordinates are (0, 0) and (6, 6).
Change in y = 6 - 0 = 6
Change in x = 6 - 0 = 6
Slope = change in y / change in x = 6 / 6 = 1 foot per second
For Object C:
The coordinates are (0, 0) and (6, 3).
Change in y = 3 - 0 = 3
Change in x = 6 - 0 = 6
Slope = change in y / change in x = 3 / 6 = 0.5 feet per second
Based on the calculations, Object A is the only one moving at a rate of 2 feet per second. So the correct answer is "object A".
To determine which object is moving at a rate of 2 feet per second, we need to look at the slopes of the lines on the graph. The slope of a line represents the rate of change or the rate at which the y-coordinate is changing with respect to the x-coordinate.
For object A, the line passes through the points (0, 0) and (3, 6). The change in y-coordinate (distance) over the change in x-coordinate (time) is (6 - 0) / (3 - 0) = 2.
So, object A is moving at a rate of 2 feet per second.
For object B, the line passes through the points (0, 0) and (6, 6). The change in y-coordinate over the change in x-coordinate is (6 - 0) / (6 - 0) = 1.
So, object B is not moving at a rate of 2 feet per second.
For object C, the line passes through the points (0, 0) and (6, 3). The change in y-coordinate over the change in x-coordinate is (3 - 0) / (6 - 0) = 0.5.
So, object C is not moving at a rate of 2 feet per second.
Therefore, only object A is moving at a rate of 2 feet per second.