Question

Find the correlation coefficient of the following linear equation using technology (such as GeoGebra). For your r-value, use the first two decimal places.

y=43x−4


2.66
2.66

0.90
0.90

1.00
1.00

−0.99
negative 0.99

Answer 1

To determine the correlation coefficient \( r \) for the linear equation \( y = 43x - 4 \), we can analyze the characteristics of the equation.

This is a straight line, and the correlation coefficient \( r \) reflects the strength and direction of a linear relationship between the variables. Here are a few key points:

1. If \( r = 1 \), there is a perfect positive linear relationship.
2. If \( r = -1 \), there is a perfect negative linear relationship.
3. Values closer to 0 indicate weaker linear relationships.

Since \( y = 43x - 4 \) represents a linear function with a positive slope (43), this means that as \( x \) increases, \( y \) also increases in a perfect linear fashion.

Therefore, the correlation coefficient \( r \) for this linear function is 1 (indicating a perfect positive correlation).

The correct answer from the choices provided is:

**1.00**