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=\frac{x}{y} \\ \frac{x_1}{y_1}=\frac{x_2}{y_2}=\frac{x_3}{y_3}\ldots\frac{x_n}{y_n} \end{gathered}$$\begin{gathered} x_1=10 \\ y_1=3 \\ k=\text{?} \\ k=\frac{x}{y}=\frac{10}{3} \end{gathered}$

now we can find y2 when x = - 6

$\begin{gathered} k=\frac{x}{y} \\ k=\frac{10}{3} \\ \frac{10}{3}=\frac{-6}{y} \\ \text{cross multiply both sides and solve for y} \\ 10\times y=3\times-6 \\ 10y=-18 \\ y=-\frac{18}{10} \\ y=-\frac{9}{5} \end{gathered}$

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