Look at the figure carefully. Notice what changes from figure to figure to identify the pattern.
y=2x+3
Practice makes perfect
To find the rule, let's consider the differences between the existing figures.
As we can see, each figure has two more tiles on the right side than the previous one. If we call the number of an arbitrary figure x and the number of tiles in that figure y, we can observe the change in x and y between figures.
Since the pattern grows at a constant rate, we know that the equation is linear. Therefore, let's use the slope-intercept form to write the rule.
y=mx+ b
The value of the slope m is found by observing the change in y and the change in x between the figures.
m=Δ y/Δ x=2/1=2
Now that we know m=2, we can write a partially completed equation.
y=2x+ 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 into the equation and solving for b. Let's use (2,7).
