1. the temperature of an ice cube increases until it starts to melt. while it melts, its temperature stays constant. which graph best shows the situation? (graphs a, b, c with temperature vs time axes)
2. mike and claudia rode a bus 15 miles to a wildlife park. they waited in line to ride a train, which took them on a 3 - mile ride around the park. after the train ride, they ate lunch, and then they rode the bus home. sketch a graph to show the distance mike and claudia traveled compared to time. use your graph to find the total distance traveled.
independent practice
3. the ink in a printer is used until the ink cartridge is empty. the cartridge is refilled, and the ink is used up again. which graph best shows the situation? (graphs a, b, c with amount of ink vs time axes)
4. on her way from home to the grocery store, a 6 - mile trip, veronica stopped at a gas station to buy gas. after filling her tank, she continued to the grocery store. she then returned home after shopping. sketch a graph to show the distance veronica traveled compared to time. use your graph to find the total distance traveled.
practice and problem solving
5. describe a situation that fits the graph at right. (graph with elevation vs time axes)
6. lynn jogged for 2.5 miles. then she walked a little while before stopping to stretch. sketch a graph to show lynn’s speed compared to time.
7. on his way to the library, jeff runs two blocks and then walks three more blocks. sketch a graph to show the distance jeff travels compared to time.

Question

Accepted Answer

### Question 1
# Explanation:
## Step1: Analyze the temperature change
The ice cube's temperature increases (rising line) until melting, then stays constant (horizontal line) while melting.
## Step2: Compare with graphs
- Graph A: Rises then horizontal (matches: increase then constant).
- Graph B: Decreases then constant (doesn't match, ice warms, not cools).
- Graph C: Rises then falls (doesn't match, temp should stay constant when melting, not fall).
# Answer: Graph A

### Question 2
# Explanation:
## Step1: Break down the journey
- Bus to park: 15 miles (distance increases with time).
- Wait in line: distance constant (horizontal line).
- Train ride: 3 miles (distance increases again).
- Eat lunch: distance constant.
- Bus home: 15 miles (distance increases back to total? Wait, no—total distance is sum of all trips: $ 15 + 3 + 15 = 33 $ miles. Wait, the bus ride to park is 15, train 3, bus home 15. So total distance: $ 15 + 3 + 15 = 33 $ miles.
## Step2: Sketch the graph
- First segment: increasing from 0 to 15 (time vs distance).
- Second: horizontal (waiting).
- Third: increasing from 15 to $ 15 + 3 = 18 $ (train ride).
- Fourth: horizontal (lunch).
- Fifth: increasing from 18 to $ 18 + 15 = 33 $ (bus home).
# Answer: The total distance traveled is 33 miles.

### Question 3
# Explanation:
## Step1: Analyze ink usage
- Ink starts full, decreases to 0 (first segment: decreasing line).
- Cartridge refilled: ink jumps back to full (vertical line up).
- Ink used again: decreases to 0 (second decreasing line).
## Step2: Compare with graphs
- Graph A: Ink stays constant then increases (doesn't match: ink should decrease first, not stay constant).
- Graph B: Decreases to 0, jumps to full, decreases to 0 (matches: use, refill, use).
- Graph C: Decreases in two steps (doesn't match, refill should be a jump, not a small drop).
# Answer: Graph B

### Question 4
# Explanation:
## Step1: Break down the journey
- Home to gas station: distance increases (part of 6-mile trip).
- Stop at gas station: distance constant (horizontal line).
- Gas station to grocery: distance increases to 6 miles.
- Shop: distance constant.
- Return home: distance increases back to $ 6 + 6 = 12 $ miles (total distance: $ 6 + 6 = 12 $ miles, since she goes 6 to store and 6 back).
## Step2: Calculate total distance
Total distance = distance to store + distance back = $ 6 + 6 = 12 $ miles.
# Answer: The total distance traveled is 12 miles.

### Question 5
# Brief Explanations:
The graph has segments: constant elevation, then increase, then constant, then decrease, then increase. A possible situation: A hiker walks on flat ground (constant elevation), then climbs a hill (elevation increases), rests (constant), descends a hill (elevation decreases), then walks on a slightly rising path (elevation increases a bit).
# Answer: Example: A hiker’s elevation over time: flat walking, climbing a hill, resting, descending, then gentle ascent. (Answers vary, but should match the graph’s shape: constant, increase, constant, decrease, increase.)

### Question 6
# Explanation:
## Step1: Analyze speed over time
- Jogging: higher speed (constant, since jogging speed is steady) → horizontal line at higher speed.
- Walking: lower speed (constant, steady walking) → horizontal line at lower speed.
- Stopping to stretch: speed 0 → horizontal line at 0.
## Step2: Sketch the graph
- First segment: horizontal (jogging speed, e.g., $ v_1 $).
- Second: horizontal (walking speed, $ v_2 < v_1 $).
- Third: horizontal at 0 (stretching).
# Answer: (Graph sketch: three horizontal segments: high (jog), lower (walk), 0 (stretch), over time.)

### Question 7
# Explanation:
## Step1: Analyze distance over time
- Running two blocks: distance increases with time (steeper line, since running is faster than walking).
- Walking three blocks: distance increases with time (less steep line, slower speed).
## Step2: Sketch the graph
- First segment: steeper increasing line (running, 2 blocks).
- Second segment: less steep increasing line (walking, 3 blocks).
# Answer: (Graph sketch: two increasing segments, first steeper (running), second less steep (walking), over time.)

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QUESTION IMAGE

Question

Explanation:

Question 1

Step1: Analyze the temperature change

Step2: Compare with graphs

Step1: Break down the journey

Step2: Sketch the graph

Step1: Analyze ink usage

Step2: Compare with graphs

Answer:

Question 2