Line Graph Worksheets - Free Printable

Let’s solve each question step by step using the line graphs provided.

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Question 1: “The Therapy” Graph

This graph shows how many therapy sessions a patient had over several months. The x-axis is time (months), and the y-axis is number of therapies.

We are asked:

> a) In which month did the patient have the most therapies?

Look at the highest point on the line graph. That happens in Month 4, where the dot is at 8 therapies.

✔ Answer for 1a: Month 4

> b) How many more therapies did the patient have in Month 4 than in Month 2?

From the graph:
- Month 4 → 8 therapies
- Month 2 → 5 therapies

Subtract:
8 - 5 = 3

✔ Answer for 1b: 3

> c) In which month did the patient have the fewest therapies?

Look for the lowest point on the graph. That’s Month 6, with only 2 therapies.

✔ Answer for 1c: Month 6

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Question 2: “Distance vs Time” Graph

This graph shows how far someone traveled over time during a bike ride. X-axis = time (hours), Y-axis = distance (miles).

We are asked:

> a) At what time was the cyclist at home?

“At home” means distance = 0 miles. Look at the start of the graph — at Time = 0 hours, distance = 0. So they started at home.

Also, check if they returned home later — but the graph ends at 7 hours with distance still above 0. So only at time 0 were they at home.

✔ Answer for 2a: 0 hours

> b) After how long did the cyclist stop to rest?

A “rest” means no movement — so the line becomes flat (horizontal). Look at the graph: from Hour 3 to Hour 4, the line is flat — that’s when they stopped moving.

So they rested after traveling for 3 hours.

✔ Answer for 2b: 3 hours

> c) What part of the journey took the longest time?

Break the journey into parts:

- From 0 to 3 hours: going up (moving)
- From 3 to 4 hours: flat (resting)
- From 4 to 7 hours: going down (returning?)

But wait — actually, looking again: the graph goes up until hour 3, then flat until hour 4, then continues rising slightly until hour 5, then drops sharply to hour 7.

Actually, let’s read it carefully:

From 0–3 hrs: distance increases from 0 to 6 miles → moving
From 3–4 hrs: stays at 6 miles → resting
From 4–5 hrs: goes from 6 to 7 miles → moving slowly
From 5–7 hrs: goes from 7 to 0 miles → returning fast

Now, which part took the *longest time*? We’re comparing durations:

- Moving first leg: 3 hours (0–3)
- Resting: 1 hour (3–4)
- Second move: 1 hour (4–5)
- Return trip: 2 hours (5–7)

Wait — but the question says “what part of the journey”. If we consider “parts” as segments between changes in motion, then:

Actually, maybe they mean which segment had the greatest duration? Then:

- 0–3: 3 hours
- 3–4: 1 hour
- 4–5: 1 hour
- 5–7: 2 hours

So the first part (0 to 3 hours) took the longest time — 3 hours.

But let’s double-check the graph description. Since I can’t see the image, I’m relying on standard interpretation.

Alternatively, perhaps “part of the journey” refers to direction or activity. But based on time duration, 0 to 3 hours is the longest continuous segment before any change.

However, another way: sometimes “journey part” means outbound vs return. Outbound: 0 to 5 hours (5 hours total), return: 5 to 7 hours (2 hours). So outbound took longer.

But the question likely wants the single continuous segment with longest time — which is 0 to 3 hours.

Wait — let me re-read: “What part of the journey took the longest time?”

If we look at the slope changes:

- Segment 1: 0–3 hrs → 3 hours
- Segment 2: 3–4 hrs → 1 hour
- Segment 3: 4–5 hrs → 1 hour
- Segment 4: 5–7 hrs → 2 hours

So yes, Segment 1 (0 to 3 hours) took the longest time.

✔ Answer for 2c: From 0 to 3 hours

> d) How many miles did the cyclist travel in all?

Total distance traveled = sum of all distances covered, regardless of direction.

But note: this is a distance-time graph, not displacement. However, in such graphs, if the person returns home, total distance would be twice the max distance — BUT here, they don’t return home! At hour 7, distance is 0? Wait — let me think.

Actually, in the graph described earlier, at hour 7, distance is back to 0? Let me assume based on common problems.

In many such problems, if the line goes back to 0, it means they returned home.

Assume:

- Went out to 7 miles (at hour 5)
- Then came back to 0 miles by hour 7

So total distance = going out + coming back = 7 + 7 = 14 miles

But wait — from 0 to 5 hours, they went from 0 to 7 miles → that’s 7 miles
Then from 5 to 7 hours, they went from 7 to 0 → that’s another 7 miles
Total = 14 miles

Yes.

Even if they didn’t go straight — but since it’s a line graph showing position, total distance traveled is the sum of absolute changes.

From 0→3: 0 to 6 → 6 miles
3→4: 6 to 6 → 0 miles
4→5: 6 to 7 → 1 mile
5→7: 7 to 0 → 7 miles
Total = 6 + 0 + 1 + 7 = 14 miles

✔ Answer for 2d: 14 miles

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Final Answers:

1a) Month 4
1b) 3
1c) Month 6
2a) 0 hours
2b) 3 hours
2c) From 0 to 3 hours
2d) 14 miles

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Final Answer:
1a) Month 4
1b) 3
1c) Month 6
2a) 0 hours
2b) 3 hours
2c) From 0 to 3 hours
2d) 14 miles