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A direct variation function includes the ordered pair [tex]$(4,5)$[/tex]. Which statement is true?

A. The constant of variation [tex]$k$[/tex] is [tex]$\frac{4}{5}$[/tex].
B. The constant of variation [tex]$k$[/tex] is [tex]$\frac{5}{4}$[/tex].
C. It is not possible to determine the constant of variation from the information given.

Sagot :

GinnyAnsweridn
In a direct variation, the relationship between two variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex] is expressed by the equation [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is the constant of variation.

Given the ordered pair [tex]\((4, 5)\)[/tex]:
- [tex]\( x = 4 \)[/tex]
- [tex]\( y = 5 \)[/tex]

First, we use the direct variation equation to find the constant of variation [tex]\( k \)[/tex]. We can solve for [tex]\( k \)[/tex] by rearranging the equation [tex]\( y = kx \)[/tex] to solve for [tex]\( k \)[/tex]:
[tex]\[ k = \frac{y}{x} \][/tex]

Next, substitute the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[ k = \frac{5}{4} \][/tex]

Therefore, the constant of variation [tex]\( k \)[/tex] is [tex]\(\frac{5}{4}\)[/tex].

The correct statement is:
The constant of variation [tex]\( k \)[/tex] is [tex]\(\frac{5}{4}\)[/tex].
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