Line Graphs

📈 Line Graphs

Part 1 of 5 — What a Line Graph Shows

Topics in This Part

🔑 Key Concept: A line graph shows how something changes over time. It uses points connected by lines so you can see whether a value is going up, going down, or staying the same.

What Is a Line Graph?

A line graph is a picture of data (information) that changes. We plot a point for each measurement, then connect the points with straight lines.

Here is a line graph of how tall a bean plant grew over 5 days:

Each row of the table becomes one point on the graph. Day 1 with a height of 2 cm becomes the point $(1, 2)$. Day 4 with a height of 8 cm becomes the point $(4, 8)$.

💡 The connecting lines are not extra data — they just help your eye follow the trend from one point to the next.

The Two Axes

Every line graph has two number lines called axes:

• The x-axis runs left to right (horizontal). It usually shows time — days, hours, months, or years.
• The y-axis runs up and down (vertical). It shows what you measured — height, temperature, money, and so on.

A point is written as an ordered pair $(x, y)$: the x-value first (across), then the y-value (up).

⚠️ Order matters! $(1, 2)$ means "go across to 1, then up to 2." It is not the same as $(2, 1)$.

Concept Check 🎯

Reading an Ordered Pair

To plot or read a point, do the x-value first, then the y-value:

$(x,\ y) = (\text{across},\ \text{up})$

Example: The point $(3, 5)$ on our plant graph means "on Day 3, the plant was 5 cm tall."

Example: The point $(5, 11)$ means "on Day 5, the plant was 11 cm tall."

🔑 First number = where on the x-axis (time). Second number = where on the y-axis (the value).

Read the Points 🧮

Use the plant table from above.

1) Write the height (the y-value) for the point on Day 2. 2) Write the height (the y-value) for the point on Day 4. 3) The point $(1, 2)$ means Day 1, height $= \,?$ cm.

📈 Line Graphs

Part 2 of 5 — Reading Values From a Graph

🔑 The Skill: Given any point in time, find its value — and given any value, find when it happened. This is the most important thing a line graph lets you do.

Finding a Value at a Given Time

To read the value at a certain time:

1. Find the time on the x-axis (across the bottom).
2. Move straight up until you hit the line.
3. Move straight across to the y-axis to read the value.

We'll use this temperature graph for a single day:

Example: What was the temperature at 10 AM? Find 10 AM on the bottom, go up to the line, read across: 66°F.

💡 You can also go backward: to find when it was 72°F, start at 72 on the y-axis and trace to the matching time — 12 PM.

Concept Check 🎯

Use the temperature table from above.

Read the Temperatures 🧮

Use the temperature table.

1) Temperature at 2 PM $= \,?$ °F 2) Temperature at 4 PM $= \,?$ °F 3) Temperature at 8 AM $= \,?$ °F

Reading Between the Points

Because the points are connected, you can estimate values between the marked times. The line shows roughly what was happening in between.

Look at the climb from 10 AM (66°F) to 12 PM (72°F). Halfway between them is 11 AM. Since the line rises steadily from 66 to 72, at 11 AM the temperature was about 69°F — right in the middle.

⚠️ This is an estimate, not an exact reading. We only measured at 10 AM and 12 PM; the line just suggests what likely happened at 11 AM.

Concept Check 🎯

📈 Line Graphs

Part 3 of 5 — Trends: Up, Down, and Flat

🔑 Big Idea: The slant of each line segment tells a story. Up means increasing, down means decreasing, and flat means staying the same.

Reading the Slant

Back to our plant:

From Day 2 to Day 3 the height stays at 5 cm — the line is flat (no growth). From Day 3 to Day 4 it climbs from 5 to 8 — the line slants up.

💡 A flat line does not mean "nothing is there." It means the value held steady.

Describe the Trend 🔽

Use the plant heights: Day 1 = 2, Day 2 = 5, Day 3 = 5, Day 4 = 8, Day 5 = 11 (cm).

How Much Did It Change?

To find the change between two points, subtract:

$\text{change} = \text{later value} - \text{earlier value}$

A positive answer means it went up. A negative answer means it went down. Zero means it was flat.

Example: From Day 1 (2 cm) to Day 2 (5 cm): $5 - 2 = 3 \text{ cm taller}$

Example: From Day 4 (8 cm) to Day 5 (11 cm): $11 - 8 = 3 \text{ cm taller}$

🔑 Always do later minus earlier. If the result is negative, the value dropped.

Find the Change 🧮

Plant heights (cm): Day 1 = 2, Day 3 = 5, Day 4 = 8, Day 5 = 11.

1) Change from Day 1 to Day 3: $5 - 2 = \,?$ cm 2) Change from Day 3 to Day 5: $11 - 5 = \,?$ cm 3) Change from Day 4 to Day 5: $11 - 8 = \,?$ cm

Concept Check 🎯

Plant heights (cm): Day 1 = 2, Day 2 = 5, Day 3 = 5, Day 4 = 8, Day 5 = 11.

📈 Line Graphs

Part 4 of 5 — Answering Questions With Data

🔑 Putting It Together: Real questions ask you to find the highest value, the lowest value, the total change, or to compare two lines. Let's practice each.

Highest, Lowest, and Total Change

We'll use the temperature data again:

• Highest temperature = the top point on the graph = 72°F (at 12 PM).
• Lowest temperature = the bottom point = 60°F (at 8 AM).
• Range (how spread out) = highest − lowest = $72 - 60 = 12$°F.

The graph also shows the shape of the day: it warmed up all morning, peaked at noon, then cooled down all afternoon.

💡 The peak (turning point) is where the line stops going up and starts going down — here, 12 PM.

Highest, Lowest, Range 🧮

Temperatures (°F): 8 AM = 60, 10 AM = 66, 12 PM = 72, 2 PM = 70, 4 PM = 64.

1) What was the highest temperature? $\,?$ °F 2) What was the lowest temperature? $\,?$ °F 3) Range $=$ highest $-$ lowest $= 72 - 60 = \,?$ °F

Comparing Two Lines

Sometimes a graph has two lines so you can compare. Suppose two friends saved money over 4 weeks:

Where the two lines cross, the friends had the same amount: in Week 3, both had $10.

After the crossing point, Leo's line is higher, so by Week 4 Leo had more ($16 vs. $12).

🔑 The point where two lines meet is where the two values are equal.

Compare the Savers 🔽

Mia: Wk1 = $5, Wk2 = $8, Wk3 = $10, Wk4 = $12. Leo: Wk1 = $2, Wk2 = $6, Wk3 = $10, Wk4 = $16.

Concept Check 🎯

Mia: Wk1 = $5, Wk2 = $8, Wk3 = $10, Wk4 = $12.

📈 Line Graphs

Part 5 of 5 — Building a Graph & Mastery Check

You can now read points, follow trends, find changes, and compare lines. In this last part you'll build a graph from a table, then take the Exit Quiz.

Building a Line Graph (4 Steps)

To turn a table of data into a line graph:

1. Label the axes. Time on the x-axis (across), the measured value on the y-axis (up).
2. Choose a scale. Pick even steps for the y-axis (like 0, 2, 4, 6, …) that reach your biggest value.
3. Plot each point as $(\text{time},\ \text{value})$ — across first, then up.
4. Connect the points in order, left to right, with straight lines.

Example table (rain in a town):

Plot $(\text{Mar}, 4)$, $(\text{Apr}, 6)$, $(\text{May}, 3)$, then connect. The line goes up from March to April, then down from April to May.

⚠️ Always plot the points in time order and connect them left to right — don't skip around.

Plot the Rain Data 🔽

Rain: Mar = 4 in, Apr = 6 in, May = 3 in.

Changes in the Rain Data 🧮

Rain (in): Mar = 4, Apr = 6, May = 3.

1) Change from Mar to Apr: $6 - 4 = \,?$ in 2) Highest rainfall amount $= \,?$ in 3) Lowest rainfall amount $= \,?$ in

Quick Reference

🔑 A line graph turns a list of numbers into a story you can see: when it rose, when it fell, and when it held steady.

Exit Quiz ✅

Answer all three to finish the lesson. Use the temperature data: 8 AM = 60°F, 10 AM = 66°F, 12 PM = 72°F, 2 PM = 70°F, 4 PM = 64°F.