Suppose that y varies inversely with x, and =y−5 when =x−8.(a)Writeaninversevariationequationthatrelatesxandy.Equation: (b)=Findywhenx4.=y

The question seems to be a bit jumbled, but I'll try to interpret it as best as I can.

It seems like you're saying that y varies inversely with x, and y = -5 when x = -8. You're asking for an inverse variation equation that relates x and y, and then you want to find y when x = 4.

(a) Inverse variation means y = k/x, where k is the constant of variation. We can find k by plugging in the values of x and y that we know (x = -8, y = -5):

-5 = k / -8

Multiplying both sides by -8, we get k = 40.

So, the inverse variation equation that relates x and y is y = 40/x.

(b) To find y when x = 4, we substitute x = 4 into the equation:

y = 40 / 4 = 10.