   SEARCH HOME Math Central Quandaries & Queries  Question from Mel, a student:

Hello! Can you please show me how to do this question?

This table shows the linear relationship between an aeroplane's height (above sea level) and the outside air temperature.

 h (cm) 120 340 480 600 1040 T (degrees C) 14.28 12.96 12.12 11.4 8.76

Find the gradient and vertical intercept of the function. Write the formula for T.

Thank you! Hi Mel,

You are looking for an equation of a line in the form y = mx + b but in your problem the variables are T and h so you want an equation of the form T = mh + b where m is the slope or gradient of the line and b is the vertical intercept (the y-intercept). In this equation T is in degrees C and h is in cm so the units of m are (degrees C)/cm, degrees C per centimeter.

Use two points in the table below to calculate m. Check with other pairs of points to verify that these points actually lie on a line. Use this value of m and one of the points in the table to write the equation T = mh + b.

 h (cm) 120 340 480 600 1040 T (degrees C) 14.28 12.96 12.12 11.4 8.76

Write back if you need more assistance,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.