Use the image to answer the question.

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

object A
object A

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 B

Answer 1

To determine which object would reach 100 feet in the least amount of time, we need to analyze the slopes of the lines represented by each object.

1. Object A: The line goes through the points (0, 0) and (3, 6), giving it a slope of 6/3 = 2 feet per second.

2. Object B: The line goes through the points (0, 0) and (6, 6), resulting in a slope of 6/6 = 1 foot per second.

3. Object C: The line goes through the points (0, 0) and (6, 3), providing a slope of 3/6 = 0.5 feet per second.

Now, let's calculate the time it takes each object to reach 100 feet.

• For Object A: At a rate of 2 feet per second, it takes 100 feet / 2 feet per second = 50 seconds.
• For Object B: At a rate of 1 foot per second, it takes 100 feet / 1 foot per second = 100 seconds.
• For Object C: At a rate of 0.5 feet per second, it takes 100 feet / 0.5 feet per second = 200 seconds.

Thus, Object A reaches 100 feet in the least amount of time, which is 50 seconds.

Final answer: object A.