Question

2. Determine whether y varies directly with x. If so, find the constant of variation and write the equation.хy-6N-93-155noOyes; k = -3 and y = -3XOyes;3 andOy--33 andyes;

Answer 1

hello

the values given are

`\begin{gathered} x\text{ y} \\ -6\text{ 2} \\ -9\text{ 3} \\ -15\text{ 5} \end{gathered}`

now we can name the values accordingly

`\begin{gathered} x_1=-6 \\ y_1=2_{} \\ x_2=-9 \\ y_2=3 \\ x_3=-15 \\ y_3=5 \end{gathered}`

now let's see how y varies with x

when y1 = 2, x1 = -6

when y increases, x decreases, this is an inverse proportion and hence y does not varies directly with x.

now let's find the constant of proportionality.

note: the value of x increases negatively and y increases

`\begin{gathered} y\propto-(1)/(x) \\ y_1=2 \\ x_1=-6 \\ y\propto-(1)/(x) \\ y=-(k)/(x) \\ -k=yx \\ k=-yx \\ k=-(y_1* x_1) \\ k=-(2*6) \\ k=-12 \end{gathered}`