Steeper line, greater change
Same step across, different step up. The steeper segment goes up more.
Which year grew more?
A village puts up solar panels. The line graph shows how many panels it has at the end of each year.
Which year had the bigger increase?
What this lesson covers
The idea
On a line graph, the steeper a line segment is, the greater the increase it shows between the two points.
Which year grew more?
A village puts up solar panels. The line graph shows how many panels it has at the end of each year.
Which year had the bigger increase?
- 2022 to 2023
- 2023 to 2024
- Both are the same
Drag the middle dot
The first and last dots stay. Drag the 2023 dot up and down. The steps under each segment show one year across and the increase up.
Steeper means a bigger step up
On a line graph, the steeper a line segment is, the greater the increase it shows between the two points.
Each segment covers one year: the step across is always the same. Only the step up changes. A steeper segment climbs more in the same year.
The panels were 40 in 2022, 110 in 2023 and 160 in 2024. 110 − 40 = 70 160 − 110 = 50 The first segment is steeper, and 70 is more than 50.
A flat segment goes up by 0: no increase. The book compares two years in the same way: it looks at which segment is steeper.
Notes
On a line graph, the steeper a line segment is, the greater the increase it shows between the two points.
Check yourself
Which segment shows the greatest increase in trees planted?
A school had 300 students in 2022, 360 in 2023 and 480 in 2024. On a line graph, which segment is steeper?
The line passes through 40 in 2022, 90 in 2023 and 160 in 2024. By how much does it increase from 2023 to 2024?
Answer: 70
160 − 90 = 70. This segment is steeper than 2022 to 2023, which goes up by only 90 − 40 = 50.
Which segment shows the greatest increase in the number of students?
- 2020 to 2021. That segment goes up by 25. Another one is steeper.
- 2021 to 2022 — correct. Yes! It is the steepest segment: it goes up by 35, from 45 to 80.
- 2022 to 2023. That segment goes up by 20. It is less steep than 2021 to 2022.
- 2023 to 2024. That is the flattest segment. It goes up by only 10.
- 2022 to 2023. That increase is 360 − 300 = 60. The other one is 480 − 360 = 120, which is more.
- 2023 to 2024 — correct. Yes! The increase is 480 − 360 = 120, more than 60 from 2022 to 2023. A bigger increase means a steeper segment.
- Both are equally steep. The increases are 60 and 120. Equal increases would give equally steep segments.
- 2021 to 2022. It goes up by 50. The segment after it is steeper.
- 2022 to 2023 — correct. Yes! It is the steepest segment: it goes up by 70, from 70 to 140.
- 2023 to 2024. It is the highest segment, but almost flat: it goes up by only 10. Steepness shows the increase, not height.