Exercise 99 Page 617

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 $3$ and Figure $4 .$

Since the pattern grows at a constant rate, we know that the equation is linear.

y = m x + b

From the table, we see that the rate of change between Figure

3

and Figure

4

increases by

2

which can be translated into a slope of

2 .

y = 2 x + 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,

(3, 11)

or

(4, 13),

into the equation and solving for

b .

y = 2 x + b

SubstituteII

$x = 3$ , $y = 11$

11 = 2 (3) + b

▼

Solve for

b

Multiply

11 = 6 + b

SubEqn

$LHS - 6 = RHS - 6$

5 = b

RearrangeEqn

Rearrange equation

b = 5

Substituting both of the known values into the equation, we have

y = 2 x + 5 .

By substituting

x = 50

into the equation, we can calculate the number of tiles in this figure.

y = 2 x + 5

Substitute

$x = 50$

y = 2 (50) + 5

Multiply

y = 100 + 5

AddTerms

Add terms

y = 105

There are

105

tiles in Figure

50 .