Question

Which function has the greatest constant of variation?


A
x
8
9
10
11
y
20
22.5
25
27.5



B
x
1
2
3
4
y
3.2
6.4
9.6
12.8




C
On coordinate plane C, a line goes through points (0, 0) and (3, 1).




D
On coordinate plane D, a line goes through points (0, 0) and (1, 2).

A
B
C
D

Answer 1

To determine which function has the greatest constant of variation, we first need to find the constant of variation (also known as the slope) for each option.

**A:**
Given points:
- (8, 20)
- (9, 22.5)
- (10, 25)
- (11, 27.5)

Calculate the slope between the first two points:
\[ \text{slope} = \frac{22.5 - 20}{9 - 8} = \frac{2.5}{1} = 2.5 \]

Check another pair:
\[ \text{slope} = \frac{25 - 22.5}{10 - 9} = \frac{2.5}{1} = 2.5 \]
The slope is consistent, so the constant of variation for A is 2.5.

**B:**
Given points:
- (1, 3.2)
- (2, 6.4)
- (3, 9.6)
- (4, 12.8)

Calculate the slope between the first two points:
\[ \text{slope} = \frac{6.4 - 3.2}{2 - 1} = \frac{3.2}{1} = 3.2 \]

Check another pair:
\[ \text{slope} = \frac{9.6 - 6.4}{3 - 2} = \frac{3.2}{1} = 3.2 \]
The slope is consistent, so the constant of variation for B is 3.2.

**C:**
The line goes through (0, 0) and (3, 1). The slope is:
\[ \text{slope} = \frac{1 - 0}{3 - 0} = \frac{1}{3} \]
So the constant of variation for C is \( \frac{1}{3} \).

**D:**
The line goes through (0, 0) and (1, 2). The slope is:
\[ \text{slope} = \frac{2 - 0}{1 - 0} = 2 \]
So the constant of variation for D is 2.

**Summary of Constants of Variation:**
- A: 2.5
- B: 3.2
- C: \( \frac{1}{3} \) (approximately 0.33)
- D: 2

The function with the greatest constant of variation is **B** with a constant of variation of **3.2**.