Which equation is not a function? $x=8 y-5$ $x+y=-4$ $9 x=y^{2}+5$ $y=8 x^{2}-8 x+3$

Step 1 ：A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. In other words, for every x-value there is exactly one y-value. This is also known as the vertical line test. If a vertical line intersects the graph more than once for any given x-value, the graph does not represent a function.

Step 2 ：We are given four equations: \(x=8y-5\), \(x+y=-4\), \(9x=y^{2}+5\), and \(y=8x^{2}-8x+3\).

Step 3 ：Looking at the equations, the third equation \(9x = y^2 + 5\) is not a function because for a given x-value, there can be two possible y-values (one positive and one negative). This is because we are squaring the y-value, which can result in the same x-value for a positive and negative y-value.

Step 4 ：The results of the calculations confirm the initial thought. The third equation \(9x = y^2 + 5\) is not a function because it has two solutions for y, which means that for a given x-value, there can be two possible y-values. This violates the definition of a function where for every x-value there should be exactly one y-value.

Step 5 ：\(\boxed{\text{Final Answer: The equation that is not a function is } 9x = y^2 + 5}\)