Chapter 8.1 Solving Equations by Graphing

Page 252- Carina’s Problem Carina wants to determine the area of a garden. The garden has 32 border tiles. The garden and border tiles are part of this pattern of squares. Carina uses the variable “n” to represent the are of the garden. We must find the area of the garden (it will be all the land inside the tiles)

What do we know from looking at the first garden? There are always 6 tiles on the left and right side combined. This leaves two tiles in the middle and when we increase our area, we will be expanding from the middle because the 6 end tiles never change in their amount. We also know there are 32 total border tiles. This means our formula is 2n+6=32 It also means 2n+6 and 32 both describe the number of border tiles.

To find the area, we create a table of values Area of the garden (term number)Number of border tiles (term value) n A table of values will allow us to see what the area will be based on which numbers we substitute for “n”. Remember our goal is find out how big the garden area will be when we have 32 tiles. Our formula is 2n+6 and the number we need is 32. We are looking for a “solution to an equation”.

My Table of Values Area of the garden (term number)Number of border tiles (term value)

My Scatter Plot