Steepness is a number
A school tank's depth (cm) is read every hour for eight hours. A graph joins the readings in a line. In the lab, pick two hours and find the rate.
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- First 4 hours: depth drops from 60 to 43.
- Last 4 hours: depth drops from 43 to 25.
Turn steep into a number
A line is steeper when it changes more in each step. The change is how far the depth falls. The steps are the hours a stretch of the line covers.
Rule: On one graph, steepness is the change divided by the steps.
In the first four hours, the depth falls 60 − 43 = 17 cm. Divide by the 4 hours: 17 ÷ 4 = 4.25 cm an hour. In the last four hours, it falls 43 − 25 = 18 cm. Divide by the 4 hours: 18 ÷ 4 = 4.5 cm an hour. The last four hours are steeper.
Take one hour in which the depth falls 6 cm. That is 6 ÷ 1 = 6 cm an hour. It is steeper than both.
A join is a guess, not a reading
Another tank is read only at hour 0 and hour 4. Both readings are 200 litres. The joined line is flat. But the tank may have reached 460 litres in between. A join cannot tell you what happened between two readings.