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Jakita examines the ordered pairs [tex]\(\left(\frac{3}{4}, \frac{2}{3}\right), \left(\frac{1}{4}, 2\right), \left(1, \frac{1}{2}\right),\)[/tex] and [tex]\(\left(\frac{1}{2}, 1\right)\)[/tex] and determines the points form a direct variation with a [tex]\(k\)[/tex] value of [tex]\(\frac{1}{2}\)[/tex].

Which statements about Jakita's conclusion are true? Select two options.

A. The points actually represent an inverse variation.
B. The [tex]\(k\)[/tex] value of the direct variation is actually 2.
C. The ordered pairs can be represented by the function [tex]\(y=\frac{x}{2}\)[/tex].
D. The ordered pairs can be represented by the function [tex]\(y=\frac{1}{2x}\)[/tex].
E. As one quantity increases, the other also increases.



Answer :

GinnyAnswer
To determine which statements about Jakita's conclusion are true, let's analyze each statement based on the results:

1. The points actually represent an inverse variation.
- An inverse variation means that as one quantity increases, the other decreases such that the product of the two quantities is constant. The given results show that this statement is true.

2. The [tex]$k$[/tex] value of the direct variation is actually 2.
- For direct variation, the relationship is [tex]\( y = kx \)[/tex]. If [tex]\( k = 2 \)[/tex], [tex]\( y \)[/tex] should be double [tex]\( x \)[/tex]. This statement is shown to be false.

3. The ordered pairs can be represented by the function [tex]\( y = \frac{x}{2} \)[/tex].
- This means the [tex]\( y \)[/tex]-value is half the [tex]\( x \)[/tex]-value. The analysis shows this relationship is false.

4. The ordered pairs can be represented by the function [tex]\( y = \frac{1}{2x} \)[/tex].
- This implies that [tex]\( y \)[/tex] is the result of 1 divided by twice the [tex]\( x \)[/tex]-value. The given results prove this statement to be true.

5. As one quantity increases, the other also increases.
- For this to be true, we would need to see a consistent direct relationship between the increases in both variables. However, the results show this to be false.

Based on our analysis, the two true statements about Jakita's conclusion are:
- The points actually represent an inverse variation.
- The ordered pairs can be represented by the function [tex]\( y = \frac{1}{2x} \)[/tex].