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 is moving at a rate of 2 feet per second?

(1 point)
Responses

object B
object B

object C
object C

all of the objects
all of the objects

object A

Answer 1

To determine which object is moving at a rate of 2 feet per second, we need to analyze the slopes of the lines based on the coordinates given.

1. Object A: It passes through the points (0, 0) and (3, 6). The slope (rate of change) can be calculated as: \[ \text{slope of A} = \frac{6 - 0}{3 - 0} = \frac{6}{3} = 2 \text{ feet per second.} \]

2. Object B: It passes through the points (0, 0) and (6, 6). The slope is: \[ \text{slope of B} = \frac{6 - 0}{6 - 0} = \frac{6}{6} = 1 \text{ feet per second.} \]

3. Object C: It passes through the points (0, 0) and (6, 3). The slope is: \[ \text{slope of C} = \frac{3 - 0}{6 - 0} = \frac{3}{6} = 0.5 \text{ feet per second.} \]

Based on these calculations:

• Object A moves at a rate of 2 feet per second.
• Object B moves at a rate of 1 feet per second.
• Object C moves at a rate of 0.5 feet per second.

Thus, the object moving at a rate of 2 feet per second is object A.