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 C
object C
object B
object B
all of the objects
all of the objects
object A
object A
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My answers are:
1: object A
2: 2 to 1
3: 10 mph
4: $0.40
and 5: Ike will earn $50 more than Greg (GREEEEEEGGGOORRRYYYY)
To determine which object is moving at a rate of 2 feet per second, we need to compare the slope of the lines. The slope of a line represents the rate at which the distance changes with respect to time.
Let's calculate the slope of each line:
For object A:
The line passes through the points (0,0) and (3,6).
The slope of the line is (change in y)/(change in x) = (6-0)/(3-0) = 6/3 = 2.
For object B:
The line passes through the points (0,0) and (6,6).
The slope of the line is (change in y)/(change in x) = (6-0)/(6-0) = 6/6 = 1.
For object C:
The line passes through the points (0,0) and (6,3).
The slope of the line is (change in y)/(change in x) = (3-0)/(6-0) = 3/6 = 1/2.
From the calculations above, we can see that the slope of object A is 2, indicating a rate of 2 feet per second. Therefore, the answer is:
Object A.
To determine which object is moving at a rate of 2 feet per second, we need to look at the slope of the lines on the graph.
The slope of a line represents the rate of change between two points. It is calculated by taking the difference in the y-coordinates divided by the difference in the x-coordinates.
Let's calculate the slopes of each line:
For line A, the coordinates are (0, 0) and (3, 6). The difference in the y-coordinates is 6 - 0 = 6, and the difference in the x-coordinates is 3 - 0 = 3. Therefore, the slope of line A is 6/3 = 2.
For line B, the coordinates are (0, 0) and (6, 6). The difference in the y-coordinates is 6 - 0 = 6, and the difference in the x-coordinates is 6 - 0 = 6. Therefore, the slope of line B is 6/6 = 1.
For line C, the coordinates are (0, 0) and (6, 3). The difference in the y-coordinates is 3 - 0 = 3, and the difference in the x-coordinates is 6 - 0 = 6. Therefore, the slope of line C is 3/6 = 0.5.
From these calculations, we can see that only line A has a slope of 2. Hence, the object represented by line A is moving at a rate of 2 feet per second.