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, if necessary.

y=5x+27
𝑦
=
5
𝑥
+
27



(1 point)
Responses

0
0 - no response given

10
10 - no response given

1
1 - no response given

−1

Answer 1

To find the correlation coefficient \( r \) for the linear equation \( y = 5x + 27 \), we can analyze the properties of the equation itself.

A linear equation of the form \( y = mx + b \) has a correlation coefficient that indicates the strength and direction of the relationship between \( x \) and \( y \). In this case:

- The slope \( m \) is 5, which indicates a positive linear relationship.
- The correlation coefficient \( r \) for a perfect linear relationship is either 1 (for positive) or -1 (for negative).

Since the equation is of a perfect linear relationship (a straight line), the correlation coefficient \( r \) would be 1.

**Final Answer: 1**