Question

The variable y varies directly as x, and y = 3 when x=10, Write an equation that relates x and y. Find у when x=-6. Equation: y= (A) When x=-6, y =(B)__

Answer 1

hello

x varies directly as y and this means that as x increase, y increases likewise when x decreases, y decreases

`\begin{gathered} x\propto y \\ x=ky \\ k=(x)/(y) \\ (x_1)/(y_1)=(x_2)/(y_2)=(x_3)/(y_3)\ldots(x_n)/(y_n) \end{gathered}`
`\begin{gathered} x_1=10 \\ y_1=3 \\ k=\text{?} \\ k=(x)/(y)=(10)/(3) \end{gathered}`

now we can find y2 when x = - 6

`\begin{gathered} k=(x)/(y) \\ k=(10)/(3) \\ (10)/(3)=(-6)/(y) \\ \text{cross multiply both sides and solve for y} \\ 10* y=3*-6 \\ 10y=-18 \\ y=-(18)/(10) \\ y=-(9)/(5) \end{gathered}`

when x = -6, y = - 9/ 5