Given a straight line plotted on a graph we can estimate the values of the gradient and either using a point on the line or by estimating the y – intercept, we can find the equation of the line in the formThe most convenient form in which to analyse the relationship between two variables x and y is the linear form, and we must see if, given a suspected relationship between two variables, we can construct a linear graph from the suspected relationship.

Suppose we suspect an exponential relationship between two variables. We also have the following data.

Time, t ins |
10 |
20 |
30 |
40 |
50 |

Mass m in g |
40.3 |
27 |
18 |
12.2 |
8.1 |

Our relationship will take the formTo transform this into a straight line we take logs of both sides obtaining,We recalculate the table.

Time, t ins |
10 |
20 |
30 |
40 |
50 |

log (m) |
3.696 |
3.296 |
2.890 |
2.501 |
2.092 |

And sketch the graph:

Comparingwithwe seeso andsothen