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
In a direct variation described by the equation [tex]\( y = kx \)[/tex], [tex]\( k \)[/tex] is known as the constant of variation. To find the constant of variation for the point [tex]\((-3, 2)\)[/tex], we need to determine the value of [tex]\( k \)[/tex] that satisfies the equation when [tex]\( x = -3 \)[/tex] and [tex]\( y = 2 \)[/tex].

Given the equation [tex]\( y = kx \)[/tex]:
1. Substitute the coordinates [tex]\((-3, 2)\)[/tex] into the equation.
[tex]\[ 2 = k(-3) \][/tex]

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

Thus, the constant of variation is:
[tex]\[ k = -\frac{2}{3} \][/tex]

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