Answer:
Please review the analysis in the step-by-step duiscussion regarding how the function is written (Is it y=(1/4)x -2 or y= 1/(4x) - 2? The answers are based on some assumptions that need to be checked.
y=(1/4)x-2 is already in standard format. y = 1/(4x) is a nonlinear equation, and does not have a standard form that is obvious to me.
Explanation:
I understand that we are asked to express this equation in standard form. Standard form of a linear equation is y = mx + b, where m is the slope and b the y-intercept.
The equation, as written, is "Y=1/4x-2." The "1/4x" is unclear. As written, it means 1 divided by 4x, or 1/(4x). If the intent is to multiply 1/4 times x, it should be written as (1/4)x, to insure we know the x belongs on top, not on bottom.
I suspect the intended format is (1/4)x. If so, the equation is already in standard format,. (1/4) is the slope and - 2 is the y-intercept.
If it is written correctly, we have to rearrange to obtain standard format:
y = 1/(4x) - 2
4xy = 1 - 2(4x)
At this point we should realize that y = 1/(4x) - 2 is not a linear function. In fact, it is a crazy function (metric term, I wish). The attached graph shows it's behavior, along with the more conventional y = (1/4)x-2, which is linear.
If y = 1(4x) - 2 is the correct equation, it is unclear to me what a standard form might take. There are stand formd for nonlinear equations invloving squares, cubes, etc. This is different, and guidelines rules don't apply.