Question

Unit Rates & Proportions Unit Test
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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

object B
object B

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
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Answer 1

object a b or c

Answer 2

To determine which object would reach 100 feet in the least amount of time, we need to find the slope of each line represented in the graph. The slope represents the rate at which distance is covered over time.

1. **Object A**:
- Coordinates: (0, 0) and (3, 6)
- Slope = (change in y) / (change in x) = (6 - 0) / (3 - 0) = 6 / 3 = 2
- This means that Object A travels 2 feet per second.

2. **Object B**:
- Coordinates: (0, 0) and (6, 6)
- Slope = (6 - 0) / (6 - 0) = 6 / 6 = 1
- This means that Object B travels 1 foot per second.

3. **Object C**:
- Coordinates: (0, 0) and (6, 3)
- Slope = (3 - 0) / (6 - 0) = 3 / 6 = 0.5
- This means that Object C travels 0.5 feet per second.

Now let's calculate the time it takes for each object to reach 100 feet:

- **Object A**:
- Time = distance / rate = 100 ft / 2 ft/sec = 50 seconds

- **Object B**:
- Time = 100 ft / 1 ft/sec = 100 seconds

- **Object C**:
- Time = 100 ft / 0.5 ft/sec = 200 seconds

From the calculations, Object A reaches 100 feet in the least amount of time (50 seconds).

Therefore, the correct response is:
**object A**

Answer 3

The object that would reach 100 feet in the least amount of time is:

**object A**

This is based on the calculated speeds (slopes) of the lines in the graph, with Object A traveling the fastest at 2 feet per second.