Compare Proportions from Graphs & Equations Quick Check1 of 51 of 5 ItemsQuestionUse 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)Responsesobject Aobject Aobject Cobject Cobject Bobject Ball of the objectsall of the objectsSkip to navigationpage 14 of 14
The object that is moving at a rate of 2 feet per second is object A.
From the graph, we can compare the slopes of the lines labeled A, B, and C to determine which object is moving at a rate of 2 feet per second.
The slope of a line represents the rate of change between the x-axis (time in seconds) and the y-axis (distance in feet).
The slope of line A can be calculated using the formula: slope = (change in y) / (change in x). From the graph, we can see that the change in y is 6 - 0 = 6 feet, and the change in x is 3 - 0 = 3 seconds. Therefore, the slope of line A is 6 / 3 = 2 feet per second.
The slope of line B can also be calculated in the same way. Here, the change in y is 6 - 0 = 6 feet, and the change in x is 6 - 0 = 6 seconds. Therefore, the slope of line B is 6 / 6 = 1 foot per second.
The slope of line C can be calculated using the same formula as well. The change in y is 3 - 0 = 3 feet, and the change in x is 6 - 0 = 6 seconds. Thus, the slope of line C is 3 / 6 = 0.5 feet per second.
Comparing the slopes, we can see that only line A has a slope of 2 feet per second. Therefore, the correct answer is object A.
To determine which object is moving at a rate of 2 feet per second, we need to analyze the slope of the lines on the graph.
The slope of a line represents the rate of change between two points. In this case, the rate of change represents the distance (in feet) divided by the time (in seconds), which gives us the rate in feet per second.
Let's first calculate the slopes of lines A, B, and C:
Line A passes through the points (0,0) and (3,6). To calculate the slope, we use the formula: slope = (change in y) / (change in x). In this case, the change in y is 6 - 0 = 6, and the change in x is 3 - 0 = 3. Therefore, the slope of line A is 6/3 = 2.
Line B passes through the points (0,0) and (6,6). Using the same formula, the change in y is 6 - 0 = 6, and the change in x is 6 - 0 = 6. Therefore, the slope of line B is 6/6 = 1.
Line C passes through the points (0,0) and (6,3). Using the formula, the change in y is 3 - 0 = 3, and the change in x is 6 - 0 = 6. Therefore, the slope of line C is 3/6 = 0.5.
Comparing the slopes, we see that only line A has a slope of 2. Therefore, the object represented by line A is moving at a rate of 2 feet per second.
So, the correct answer is: "object A".