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

`(y-y_1)/(x-x_1) = (y_2-y_1)/(x_2-x_1)`

Using the points (30, 18) and (36, 24), we have

`(y-18)/(x-30) = (24-18)/(36-30)= (6)/(6) =1 \\ \\ \Rightarrow y-18=x-30 \\ \\ \Rightarrow y=x-30+18 \\ \\ \Rightarrow y=x-12`