If y=-8 and x= -3 what’s x when y= 6

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

step 1

Find the value of the constant of proportionality k

[tex]k=\frac{y}{x}[/tex]

For x=-3, y=-8

substitute the given values

[tex]k=\frac{-8}{-3}[/tex]

[tex]k=\frac{8}{3}[/tex]

step 2

Find the linear equation

[tex]y=\frac{8}{3}x[/tex]

step 3

Find the value of x when y=6

substitute the value of y in the linear equation

[tex]6=\frac{8}{3}x[/tex]

solve for x

[tex]x=(6)\frac{3}{8}[/tex]

[tex]x=\frac{18}{8}[/tex]

simplify

[tex]x=\frac{9}{4}[/tex]

Part 2) If y varies inversely with x, and If y=-8 and x= -3 what’s x when y= 6

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

step 1

Find the value of the constant of proportionality k

[tex]k=y*x[/tex]

For x=-3, y=-8

substitute the given values

[tex]k=(-8)(-3)[/tex]

[tex]k=24[/tex]

step 2

Find the equation

[tex]yx=24[/tex]

step 3

Find the value of x when y=6

substitute the value of y in the equation

[tex]6x=24[/tex]

solve for x

[tex]x=4[/tex]