A line graph shows a city's monthly rainfall. Between June and July the line rises steeply; between January and February it barely moves. What can you correctly conclude?
AJune and July had more total rainfall combined than January and February combined
BRainfall increased much more rapidly from June to July than from January to February
CThe exact daily rainfall for every day within each month can be read from the line
DA bar graph would display the same information more clearly
Slope represents rate of change, not total amount. A steeper slope means the quantity increased more quickly during that interval — not necessarily that the total was larger. Option A confuses steepness of change with magnitude of total. Option C is the classic misconception: line segments show trend, but values between plotted points are unknown unless you have reason to interpolate.
Question 2 Multiple Choice
A student reads a line graph where the y-axis starts at 50 instead of 0. The line rises from 55 to 60 over one month. The student says 'the value almost doubled — look how far the line went up!' What error is the student making?
ANone — a rise from 55 to 60 is proportionally close to doubling
BThe student is misled by the compressed scale: the value increased by only 5 units, nowhere near doubling
CThe student should switch to a bar graph, since line graphs are inherently misleading
DThe error is minor — the student correctly read the scale but chose the wrong comparison word
When the y-axis does not start at zero, the visual height of a change is magnified relative to the actual data change. 55 to 60 is a 5-unit increase — about 9% growth, far from doubling. The most important scale-reading habit is always checking the y-axis before interpreting how large a visual change appears. This is one of the most common ways line graphs mislead readers who skip inspecting the scale.
Question 3 True / False
A steep slope between two consecutive plotted points on a line graph means the quantity changed rapidly during that interval.
TTrue
FFalse
Answer: True
Slope is the visual encoding of rate of change. A steep line segment means the quantity rose or fell a large amount over a short time interval — which is precisely what rapid change means. A nearly flat segment signals slow or no change. This is what makes line graphs more informative than tables of values for continuous data: rates of change are immediately visible in the shape of the line.
Question 4 True / False
The line segment connecting two plotted data points on a line graph tells you the exact value of the quantity at any moment between those two points.
TTrue
FFalse
Answer: False
Line segments show a visual trend — they make direction and rate of change easier to see. But actual values between measured data points are unknown unless you have additional data or a valid reason to interpolate. If a graph shows one temperature reading per day, the line between Monday and Tuesday does not tell you the temperature at noon. The connecting line is a perceptual tool for spotting patterns, not a source of new data.
Question 5 Short Answer
Why are line graphs appropriate for displaying daily temperature over a month, but not for displaying the number of students who chose each favorite color? What property of the data determines which graph type is appropriate?
Think about your answer, then reveal below.
Model answer: Temperature is continuous data: it changes smoothly over time and values between measurements meaningfully exist. The connecting line represents a plausible trajectory through those intermediate values. Favorite colors are categorical data: the categories have no inherent order or 'between' — there is nothing between 'blue' and 'red.' A line connecting those bars would imply a continuous trend where none exists.
The key property is whether data is continuous (ordered, with meaningful intermediate values) or categorical (distinct groups with no inherent order). Line graphs are designed for continuous data; bar graphs are designed for categorical data. Using the wrong graph type doesn't just look wrong — it actively misrepresents the nature of the data being shown.