Compare Proportions from Graphs & Equations Quick Check

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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 A
object A

object C
object C

all of the objects
all of the objects

object B
object B
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Answer 1

To determine which object is moving at a rate of 2 feet per second, we need to look at the slope of each line in the graph. The slope can be calculated using the formula:

\[ \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{distance}}{\text{time}} \]

Let's evaluate each object:

1. Object A:

   • Passes through (0, 0) and (3, 6).
   • Rise = 6 feet, Run = 3 seconds.
   • Slope = \( \frac{6}{3} = 2 \) feet per second.

2. Object B:

   • Passes through (0, 0) and (6, 6).
   • Rise = 6 feet, Run = 6 seconds.
   • Slope = \( \frac{6}{6} = 1 \) foot per second.

3. Object C:

   • Passes through (0, 0) and (6, 3).
   • Rise = 3 feet, Run = 6 seconds.
   • Slope = \( \frac{3}{6} = 0.5 \) feet per second.

Based on the calculations:

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

Therefore, the answer is object A.