If the plotted points make a pattern, then the coordinates of each point may
have the same relationship between the *x* and *y* values.
In such a case, the *x* and *y* values are connected by a certain
rule.
A** linear pattern** is said to exist when the points examined form a
straight line.
Example 2
a. Plot the points in the following table on a Cartesian
plane.
b. Describe the pattern in words.
c. State the next point in the pattern.
d. Find the rule that connects *x* and *y*.
##### Solution:
b. A linear pattern exists as the points form a straight
line. The pattern shows that as the *x *value increases by 1, the *y *value increases by 2.
c. The next *x* value will be 4 and the next *y *value
will be 8. So, the next point is (4, 8).
d. By trial and error, we look for a relationship between the
values of *x* and *y*.
The above information for *x *and *y* indicates that the *y*-coordinate
is twice the *x*-coordinate. This means *y* is twice *x*.
So, the rule that connects the *x*-coordinate and the *y-*coordinate
is:
Example 3
a. Plot the following points on the Cartesian plane:
(–3, –9), (–2, –6), (–1, –3),
(0, 0), (1, 3), (2, 6), (3, 9)
b. Describe the pattern in words.
c. Find the rule that connects *x* and *y*.
##### Solution:
b. We notice that the points plotted on the Cartesian plane form a
straight line. So, a linear pattern exists. We can describe this
pattern in words as follows:
The *y*-coordinate is three times the *x-*coordinate.
This means *y* is three times *x*.
c. The rule that connects the *x*-coordinate and *y-*coordinate
is:
Example 4
a. Plot the following points on the Cartesian plane:
(–5, –7), (–4, –6), (–3, –5), (–2,
–4), (–1, –3), (0, –2), (1, –1), (2, 0), (3, 1),
(4, 2), (5, 3), (6, 4)
b. Describe the pattern in words.
c. Find the rule that connects *x* and *y*.
##### Solution:
b. We notice that the points plotted on the Cartesian plane form a
straight line. So, a linear pattern exists. We can describe this
pattern in words as follows:
The *y*-coordinate is two less than the *x*-coordinate.
c. The rule that connects the *x*-coordinate and the *y-*coordinate
is:
Key Terms
linear pattern |