To solve for the constant of variation [tex]\( k \)[/tex] in the equation where [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex], we start with the given relationship:
[tex]\[ y = kx \][/tex]
Given:
[tex]\[ y = 3 \][/tex]
[tex]\[ x = -1 \][/tex]
We can substitute these values into the equation to solve for [tex]\( k \)[/tex]:
[tex]\[ 3 = k \cdot (-1) \][/tex]
Next, isolate [tex]\( k \)[/tex] by dividing both sides of the equation by [tex]\(-1\)[/tex]:
[tex]\[ k = \frac{3}{-1} \][/tex]
Simplifying this division:
[tex]\[ k = -3.0 \][/tex]
Thus, the value of [tex]\( k \)[/tex] is:
[tex]\[ k = -3.0 \][/tex]
