Question

which of the following best describes the relationship between x and y according to the line of best fit?
a the value of y is always equal to 10.
b as x increases, y tends to increase.
c the value of y is the same for all values of x.
d there is no relationship between x and y.

Explanation:

Step1: Analyze Option A

If \(y\) is always equal to \(10\), the line of best - fit would be a horizontal line \(y = 10\). But the given line is not horizontal.

Step2: Analyze Option B

Looking at the line of best - fit, as \(x\) values (moving from left to right on the \(x\) - axis) increase, the \(y\) values (moving up on the \(y\) - axis) tend to increase. This is the characteristic of a positive - correlation (or a line with a positive slope).

Step3: Analyze Option C

If \(y\) is the same for all \(x\), the line of best - fit would be a horizontal line. Since the line is not horizontal, this option is incorrect.

Step4: Analyze Option D

The presence of a line of best - fit (which is not a horizontal or a vertical line) indicates that there is a relationship between \(x\) and \(y\).

Answer:

B. As \(x\) increases, \(y\) tends to increase.