Question

The table shows the heights in inches of trees after they have been planted. Determine the equation which relates x and y.

Height In Pot, x | Height Without Pot, y
30 | 18
36 | 24
42 | 30
48 | 36


A. y = x - 6
B. y = x - 10
C. y = x - 12
D. y = x + 6

Answer 1

To get the that relates x and y, we choose two points on the table and use the equation of a straight line as follows:

Recall that the equation of a staight line is obtained from the formula
$\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}$

Using the points (30, 18) and (36, 24), we have
$\frac{y-18}{x-30} = \frac{24-18}{36-30}= \frac{6}{6} =1 \\ \\ \Rightarrow y-18=x-30 \\ \\ \Rightarrow y=x-30+18 \\ \\ \Rightarrow y=x-12$