A line graph is a graph that connects points with line segments. The lines help to clarify the pattern of change in the values the points represent.

Line graphs are generally used to show the change in a quantity over time. A runner might record her times at each daily practice and create a line graph to help her see the pattern of improvement, or to see if there was a particular time when her times were slower or faster than usual.

To create a line graph, you need data that has been recorded. Each entry should include a date or time and a value. Let’s suppose that runner recorded her times in seconds for the 200 meters every day in April. Here is her record for the first 10 days.

Day 1 2 3 4 5 6 7 8 9 10

Time 22.71 22.68 22.50 22.43 22.37 22.19 22.04 21.97 21.91 21.89

The horizontal scale should show the day numbers, in this case up to 10, equally spaced along the axis. The vertical scale must go high enough to record all the times, so up to about 23 seconds.

Then place a dot in line with each day’s number at a height that corresponds to that day’s time in seconds on the vertical axis. Finally, connect the dots, day 1 to day 2 to day 3 and so on, using straight line segments.

You may find that your first attempt is not satisfactory. If you labeled your vertical scale from 0 to 23 seconds, the graph may look very flat. The runner’s times are only changing by a fraction of a second at a time.

A broken scale is a good idea here. Here’s what the same graph looks like if you use a broken scale, showing only 21.4 to 22.8 instead of 0 to 23. It’s much easier to see the changes in the runner’s times.

The line graph shows the monthly net profit statement for Amy’s

Antiques from January to December.

In which month was the net profit the same as the net profit in February?

What is the total net profit for the first quarter of the year (that is, January, February, and March combined)?

Which month shows the same increase in net profit, when compared with the previous month, as was shown in April when compared with March?

Which pair of consecutive months shows a combined net profit of exactly $8,800?

Which month accounts for approximately 5% of the total yearly net profit?

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