Question 689126
The general equation that should be formed is as follows:

y - A = Bsin(x - C)

where:

A stands for a vertical shift (if A is positive, move is upward; if A is negative, move is downward)

B stands for vertical stretch factor 

C stands for a horizontal shift (if C is positive, move is to the right; if C is negative, move is to the left).

We start with the sine wave in 'home' position, having equation y = sin(x) which is really as follows:

y - 0 = 1sin(x - 0)

with 

A = 0, (no vertical shift or change)

B = 1, (normal stretch factor or 'amplitude')

C = 0, (no horizontal shift or change)

so, the equation required is as follows:

y - (-8) = 4sin(x - 9) 

which can simplify to

y + 8 = 4sin(x - 9)

or, if final equation is given in the form "y in terms of x" (also called 'making y the subject'), then:

y = 4sin(x - 9) - 8