Answer:
k equals negative StartFraction 2 Over 3 EndFraction
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
we have that
For x=-3, y=2
Find the value of the constant of proportionality k
[tex]k=y/x[/tex]
substitute the value of y and x
[tex]k=-\frac{2}{3}[/tex]
The linear equation is
[tex]y=-\frac{2}{3}x[/tex]
therefore
k equals negative StartFraction 2 Over 3 EndFraction
What is the constant of variation, k, of the direct variation, y = kx, through (–3, 2)? k = -2/3
The constant of variation is the number which relates the two variables that directly proportional / inversely proportional to one another.
The direct variation definition is the mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other. The examples of direct variation problems are the number of hours you work and the amount of your paycheck.
[tex]y = kx[/tex], where [tex]k[/tex] is the constant of variation. Since [tex]k[/tex] is constant we can find [tex]k[/tex] when given any point by dividing the [tex]y[/tex]-coordinate by the [tex]x[/tex]-coordinate.
The equation of a line is [tex]y=kx[/tex] (1)
According to the question, the line is passes through [tex](-3,2)[/tex]
Therefore, the point will be satisfy the equation of line.
Put[tex]x=-3[/tex] and [tex]y=2[/tex] in equation
Therefore the required value of constant of variation, [tex]k= \frac{-2}{3}[/tex]
Grade: 5
Subject: Math
Chapter: the constant of variation
Keywords: the constant of variation, Fraction, equals, the direct variation, Over
