Table 1 shows the linear relationship between the two variables.
What is linear relationship?
A linear relationship is one in which two variables have a direct connection, which means if the value of x is changed, y must also change in the same proportion.
According to the given question.
We have some tables. Which represents the relationship between the two variables x and y.
Since,
If x is linearly related to y then the slope will same for every points.
For the
Table 1.
For the points (9, 13) and (14, 16)
[tex]slope = \frac{16-13}{14-9}[/tex]
[tex]\implies slope = \frac{3}{5}[/tex]
For the points (14, 16) and (19, 19)
[tex]slope = \frac{19-16}{19-14} =\frac{3}{5}[/tex]
So we can see that the slope is same for each pair of points.
Hence, table 1 shows the linear relationship between the two variables.
Table 2:
For the points (-4, 2) and (2, 10)
[tex]slope = \frac{10-2}{2+4} =\frac{8}{6} =\frac{4}{3}[/tex]
For the points (8, 50) and (2, 10)
[tex]slope = \frac{10-50}{2-8} =\frac{-40}{-6} =\frac{20}{3}[/tex]
Since, the slope are not same. Therefore, table 2 doesn't shows the linear relationship between the two variables.
For table 3
Since the slope is changing therefore, table 3 doesn't shows the linear relationship between the two variables.
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