Answered

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What is the constant of variation, [tex]\( k \)[/tex], of the direct variation [tex]\( y = kx \)[/tex] through [tex]\((-3, 2)\)[/tex]?

A. [tex]\( k = -\frac{3}{2} \)[/tex]
B. [tex]\( k = -\frac{2}{3} \)[/tex]
C. [tex]\( k = \frac{2}{3} \)[/tex]
D. [tex]\( k = \frac{3}{2} \)[/tex]

Sagot :

GinnyAnswer
To determine the constant of variation, [tex]\( k \)[/tex], for the direct variation equation [tex]\( y = kx \)[/tex] given the point [tex]\((-3, 2)\)[/tex], follow these steps:

1. Start with the direct variation equation:
[tex]\[ y = kx \][/tex]

2. Substitute the given point [tex]\((-3, 2)\)[/tex] into the equation:
[tex]\[ 2 = k(-3) \][/tex]

3. Solve for [tex]\( k \)[/tex]:
[tex]\[ k = \frac{2}{-3} = -\frac{2}{3} \][/tex]

Therefore, the constant of variation [tex]\( k \)[/tex] is [tex]\(-\frac{2}{3}\)[/tex].

The correct answer is:
[tex]\( k = -\frac{2}{3} \)[/tex]
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