Unit Rates & Proportions Unit Test
13 of 1513 of 15 Items
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 would reach 100 feet in the least amount of time?
(1 point)
Responses
They would all reach 100 feet at the same time.
They would all reach 100 feet at the same time.
object C
object C
object A
object A
object B
object B
object C
To determine which object would reach 100 feet in the least amount of time, we need to compare the slopes of the lines A, B, and C.
The slope of a line represents the rate at which the object is moving. In this case, the vertical axis represents distance in feet, and the horizontal axis represents time in seconds.
Let's calculate the slopes for each line:
- Line A: Slope = (change in y)/(change in x) = (6-0)/(3-0) = 6/3 = 2 feet per second
- Line B: Slope = (change in y)/(change in x) = (6-0)/(6-0) = 6/6 = 1 foot per second
- Line C: Slope = (change in y)/(change in x) = (3-0)/(6-0) = 3/6 = 0.5 feet per second
Since Line C has the lowest slope (0.5 feet per second), it means that object C would reach 100 feet in the least amount of time.
Therefore, the correct answer is:
object C
To determine which object would reach 100 feet in the least amount of time, we need to compare the rates of change for each object on the coordinate plane. The rate of change represents how fast an object is moving in terms of distance (feet) over time (seconds).
Let's analyze each object:
1. Object C: The dashed line passes through coordinates (0, 0) and (6, 3). We can determine the rate of change by calculating the change in distance divided by the change in time. From (0, 0) to (6, 3), the change in distance is 3 feet, and the change in time is 6 seconds. Therefore, the rate of change for object C is 3/6 = 0.5 feet per second.
2. Object A: The solid line passes through coordinates (0, 0) and (3, 6). We can calculate the rate of change in a similar way, where the change in distance is 6 feet and the change in time is 3 seconds. The rate of change for object A is 6/3 = 2 feet per second.
3. Object B: The dotted line passes through coordinates (0, 0) and (6, 6). Again, we calculate the rate of change using the change in distance (6 feet) divided by the change in time (6 seconds). The rate of change for object B is 6/6 = 1 foot per second.
Comparing the rates of change, we can see that object A has the fastest rate of 2 feet per second, followed by object B with a rate of 1 foot per second, and object C with a rate of 0.5 feet per second.
Therefore, object A would reach 100 feet in the least amount of time compared to the other objects.