Question

The number of species of coastal dune plants in australia decreases as the latitude, in °s, increases. There are 34 species at 11°s and 26 species at 44°s.1 (a) find a formula for the number, n, of species of coastal dune plants in australia as a linear function of the latitude, l, in °s. Round the slope to four decimal places and the intercept to two decimal places.

Answer 1

We have been given that the number of species of coastal dune plants in Australia decreases as the latitude, in °s, increases.

Further we know that there are 34 species at 11°s and 26 species at 44°s.

We can express the given information at two ordered pairs as shown below:

$(n,l)=(11,34)\text{ and }(n,l)=(44,26)$

Let us find slope of the line through these points:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{26-34}{44-11}=\frac{-8}{33}=-0.2424$

Therefore, we can write the equation of line in slope intercept form as:

$n=-0.2424l+b$

Where b is the y intercept, and we can find its value using one of the two points.

$34=-0.2424(11)+b\\34=-2.67+b\\b=34+2.67=36.67$

Therefore, the required equation of the linear function is:

$n=-0.2424l+36.67$