guided practice
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?
graph a
temperature
time
graph b
temperature
time
graph c
temperature
time
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?
graph a
amount of ink
time
graph b
amount of ink
time
graph c
amount of ink
time
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
e
5. describe a situation that fits the graph at right.
elevation
time
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 (so the graph should have a rising line) until it melts, then stays constant (horizontal line).
## Step2: Compare with graphs
- Graph A: Rises then horizontal (matches the ice melting scenario).
- Graph B: Decreases then horizontal (wrong, temperature should increase).
- Graph C: Rises then falls (wrong, temperature stays constant while melting, not falls).

# Answer: Graph A

### Question 2
# Explanation:
## Step1: Analyze each segment of the trip
- Bus to park: Distance increases by 15 miles (rising line).
- Waiting in line: Distance stays constant (horizontal line).
- Train ride: Distance increases by 3 miles (rising line).
- Eating lunch: Distance stays constant (horizontal line).
- Bus home: Distance increases by 15 miles (rising line).
## Step2: Calculate total distance
Total distance = 15 (to park) + 3 (train) + 15 (home) = 33 miles.

# Answer: The total distance traveled is 33 miles.

### Question 3
# Explanation:
## Step1: Analyze ink usage
- First, ink is used until empty (decreasing line to zero).
- Then cartridge is refilled (ink jumps back to full, vertical line up).
- Then ink is used again (decreasing line to zero).
## Step2: Compare with graphs
- Graph A: Increases at the end (wrong, should decrease then refill then decrease).
- Graph B: Decreases to zero, refills (jumps up), then decreases to zero (matches).
- Graph C: Decreases, stays constant, then decreases (wrong, no refill jump).

# Answer: Graph B

### Question 4
# Explanation:
## Step1: Analyze each segment of the trip
- Home to gas station: Distance increases by some amount (rising line, let's say she drove $ x $ miles to gas, but total to store is 6, so from gas to store is $ 6 - x $).
- At gas station: Distance constant (horizontal line).
- Gas to store: Distance increases to 6 miles (rising line).
- Shopping: Distance constant (horizontal line).
- Store to home: Distance increases by 6 miles (rising line).
## Step2: Calculate total distance
Total distance = 6 (to store) + 6 (home) = 12 miles. Wait, no: Wait, she goes from home to store (6 miles), then home (6 miles). So total is $ 6 + 6 = 12 $ miles? Wait, no, the trip to store is 6 miles (home to store), then home is another 6. So total distance is $ 6 + 6 = 12 $ miles. Wait, but did she stop at gas station on the way to store? Let's re - analyze: The trip from home to store is 6 miles. She stops at gas station on the way, so the distance from home to gas is $ d $, gas to store is $ 6 - d $. Then store to home is 6 miles. So total distance is $ d+(6 - d)+6=12 $ miles.

# Answer: The total distance traveled is 12 miles.

### Question 5
# Brief Explanations:
A possible situation: A hiker starts at a certain elevation, walks on a flat path (elevation constant), then climbs a hill (elevation increases), walks on a flat plateau (elevation constant), then descends a hill (elevation decreases), and then walks on a flat path again (elevation constant). The graph has periods of constant elevation (flat walking), increasing elevation (climbing), constant (plateau), decreasing (descending), and constant (flat again), which matches the given elevation - time graph.
# Answer: A hiker starts at a constant elevation (walking on flat ground), then climbs a hill (elevation increases), walks on a flat plateau (elevation constant), descends a hill (elevation decreases), and then walks on flat ground again (elevation constant). (Other valid situations are also acceptable, e.g., an elevator moving: starts at a floor (constant elevation), moves up (elevation increases), stays at a floor (constant), moves down (elevation decreases), stays at a floor (constant).)

### Question 6
# Explanation:
## Step1: Analyze each segment of Lynn's activity
- Jogging: Higher speed (constant, so a horizontal line at higher speed for the distance of 2.5 miles. Since speed = distance/time, if she jogs 2.5 miles, the time for jogging is $ t_1=\frac{2.5}{v_{jog}} $, so the speed graph is a horizontal line at $ v_{jog} $ for $ t_1 $ time.
- Walking: Lower speed (horizontal line at lower speed for some time $ t_2 $).
- Stopping to stretch: Speed is 0 (horizontal line at 0 for time $ t_3 $).
## Step2: Sketch the graph
- First, a horizontal line at jogging speed (higher) for the time she jogged 2.5 miles.
- Then a horizontal line at walking speed (lower) for the time she walked.
- Then a horizontal line at 0 (speed) for the time she stretched.

# Answer: The graph will have three segments: a horizontal line at a higher speed (jogging) for the time corresponding to 2.5 miles, a horizontal line at a lower speed (walking) for the time she walked, and a horizontal line at speed 0 for the time she stretched. (A rough sketch would show these three horizontal segments with the first at a higher y - value, the second at a lower y - value, and the third at y = 0.)

### Question 7
# Explanation:
## Step1: Analyze each segment of Jeff's trip
- Running two blocks: Distance increases at a faster rate (steeper rising line, since running is faster than walking).
- Walking three blocks: Distance increases at a slower rate (less steep rising line, since walking is slower than running).
## Step2: Sketch the graph
- First, a steeper rising line (for running 2 blocks, distance vs time: speed is higher, so slope is steeper).
- Then a less steep rising line (for walking 3 blocks, speed is lower, so slope is less steep).

# Answer: The graph will have two segments: a steeper rising line (representing running two blocks, since running is faster, the slope is steeper) and a less steep rising line (representing walking three blocks, since walking is slower, the slope is less steep).

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 1

Step1: Analyze the temperature change

Step2: Compare with graphs

Step1: Analyze each segment of the trip

Step2: Calculate total distance

Step1: Analyze ink usage

Step2: Compare with graphs

Answer:

Question 2