a Look at the figure carefully. Notice what changes from figure to figure to identify the pattern.
B
b Since the pattern grows linearly, we can describe it with a linear equation.
A
a
B
b 51
Practice makes perfect
a Before we sketch the next two figures of the given tile pattern, let's consider the differences between the existing figures.
Look at the figures, we can notice that there is a clear pattern. Each figure has 5 more tiles on the right side than the previous figure. Each time, the bottom and top of the figure are 2 tiles longer, and the middle is 1 tile longer. Therefore, Figure 4 would have 8 tiles on its top and bottom, and 5 tiles in the middle.
Figure0 will have 5 tiles less than the Figure 1. That means this figure will be made from one tile.
b Let's call the number of an arbitrary figure x and the number of tiles in that figure y. From the information in the exercise, we can measure the change in x and y between Figure 1 and Figure 2.
Since the pattern grows at a constant rate, we know that the equation is linear.
y=mx+b
From the table, we see that the rate of change between Figure 1 and Figure 2 increases by 5 which can be translated into a slope of 5.
y=5x+b
To finalize the equation, we also need to find the y-intercept b. We can do that by substituting either of the known points, (1,6) or (2,11), into the equation and solving for b.
Substituting both of the known values into the equation, we have y=5x+1. By substituting x=10 into the equation, we can calculate the number of tiles that will be in figure 10.
