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 A
object A
object C
object C
object B
To answer this question, we need to analyze the three objects represented by the lines on the graph.
Object A is represented by the solid line passing through the points (0,0) and (3,6). Object B is represented by the dotted line passing through the points (0,0) and (6,6). Object C is represented by the dashed line passing through the points (0,0) and (6,3).
To determine which object would reach 100 feet in the least amount of time, we need to find the time it takes for each object to reach 100 feet.
We can do this by examining the relationship between the y-axis (distance in feet) and the x-axis (time in seconds). The slope of the line represents the speed at which the object is moving.
By calculating the slopes of the three lines, we can determine the rate at which each object is moving. The slope of a line can be calculated using the formula:
Slope = (change in y-coordinate) / (change in x-coordinate)
Let's calculate the slopes for each line:
For Object A:
Slope = (6 - 0) / (3 - 0) = 6 / 3 = 2
For Object B:
Slope = (6 - 0) / (6 - 0) = 6 / 6 = 1
For Object C:
Slope = (3 - 0) / (6 - 0) = 3 / 6 = 0.5
From the slopes, we can infer that Object A has a steeper slope (2), meaning it is moving faster towards 100 feet. Object B has a slope of 1, indicating it is moving at a constant speed, and Object C has the smallest slope (0.5), meaning it is moving slowest towards 100 feet.
Therefore, Object A would reach 100 feet in the least amount of time compared to Object B and Object C.