Question

The following values are collected from an experiment

y

33

38.4

46.2

What type of relationship exists between the x and y values?

(1 point)

O Linear

O Quadratic

OTriangular

O Irregular

X

5.5

6.4

7.7

Answer 1

To determine the type of relationship between the x and y values, we can examine the values presented:

- **x values:** 5.5, 6.4, 7.7
- **y values:** 33, 38.4, 46.2

We can check the pattern in y-values relative to x-values.

1. Calculate the difference in y values and the difference in x values:

- Between the first and second points:
- \( y: 38.4 - 33 = 5.4 \)
- \( x: 6.4 - 5.5 = 0.9 \)

- Between the second and third points:
- \( y: 46.2 - 38.4 = 7.8 \)
- \( x: 7.7 - 6.4 = 1.3 \)

2. Now calculate the slopes between these points:

- Slope between the first and second points:
\(\frac{5.4}{0.9} = 6\)

- Slope between the second and third points:
\(\frac{7.8}{1.3} \approx 6\)

The slopes are approximately constant. This suggests a linear relationship, as the changes in y are proportional to the changes in x.

Therefore, the type of relationship that exists between the x and y values is:

**Linear** (First option).