Question

4 - 22 continued
tile pattern #1
rule: y=
tile pattern #2
rule: y=
tile pattern #3
rule: y=
tile pattern #4
rule: y=
explore using 4 - 22 student etool (desmos).
graph each rule using the etool above. try and match
the colors of the rule with the colors of the line.
do this on
resource
page!
4 - 23a/b
the graph at right gives information about three new tile patterns.
a. what information does the circled
point (0) on the graph tell you about
tile pattern a?
b. find the growth of each tile pattern. for example, how
much does tile pattern a increase from one figure to the
next?
tile pattern a
tile pattern b
tile pattern c

Explanation:

Step1: Analyze the y - intercept for part a

In a graph of the form \(y = mx + b\) (where \(y\) is the number of tiles, \(x\) is the figure number), when \(x = 0\), \(y=b\). For tile pattern A, when the figure number \(x = 0\), the value of \(y\) (the number of tiles) is the \(y\) - intercept.

Step2: Calculate the slope (growth rate) for part b

The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For tile pattern A: Let \((x_1,y_1)=(0,8)\) and \((x_2,y_2)=(4,12)\). Then \(m_A=\frac{12 - 8}{4-0}=\frac{4}{4}=2\). For tile pattern B: Let \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(4,14)\). Then \(m_B=\frac{14 - 0}{4-0}=\frac{14}{4}=3.5\). For tile pattern C: Let \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(2,8)\). Then \(m_C=\frac{8 - 0}{2-0}=4\).

Answer:

a. When the figure number is \(0\) (the starting point), tile pattern A has \(8\) tiles.
b. Tile Pattern A: \(2\) tiles per figure; Tile Pattern B: \(3.5\) tiles per figure; Tile Pattern C: \(4\) tiles per figure.