Interpolating and extrapolating from a linear graph

0:00A 24 centimetre candle burns down 1.5 centimetres every hour.

0:06After t hours, its height in centimetres is h equals 24 minus 1.5 t.

0:14Time t goes along the horizontal axis, and height h goes up the vertical axis.

0:22We measured it every 2 hours for 8 hours: 24, 21, 18, 15 and 12 centimetres.

0:31It drops 3 centimetres every 2 hours, so the points lie on a straight line: a linear relation.

0:38Interpolating means estimating a value between the data points.

0:43How tall is the candle after 3.5 hours?

0:473.5 is a time, so start on the time axis and go straight up to the line.

0:55Then go across to the height axis. It reads about 19 centimetres.

1:00Check: 24 minus 1.5 times 3.5 is 24 minus 5.25, which is 18.75 centimetres.

1:12A common mistake is to find 3.5 on the height axis, but 3.5 is a time.

1:21Extrapolating means extending the line past the data, to estimate beyond it.

1:27The candle burns out when h is 0, where the line meets the time axis: at 16 hours.

1:35Check: 0 equals 24 minus 1.5 t, so t equals 24 divided by 1.5, which is 16.

1:47Our data stops at 8 hours. The rate could change, so a value this far past the data is less certain.

1:56Interpolate inside the data, and extrapolate beyond it with care.