Hello! I'm doing functions at the moment and we have to find the gradient and the y-intercept in an equation like y=5x+2 etc. I know how to do that and everything, but eventually we get some...

Hello! I'm doing functions at the moment and we have to find the gradient and the y-intercept in an equation like y=5x+2 etc. I know how to do that and everything, but eventually we get some harder questions where we have to switch the order of the equation so we get the Y in the beginning like it has to be! I know how to do that as well, but my question is: do we have to put in a negative sign in the equation after i've switched the order? I can give an example. y+4x=6. Now I change it to: y=4x+6 but apparently I have to put a negative/positive (depends) into the equation? Is this some rule I didn't know about? If so, how does it go? THANKS

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to change the signs of the terms if you move them from the left side to the right side, such that:

`y + 4x = 6 => y = -4x + 6`

You should notice that the term `4x` was moved from the left, where it has positive sign, to the right, with negative sign.

The steps you need to perform when you need to move one term from one side to the other, are:

`y + 4x = 6 => y + 4x - 4x = 6 - 4x` (subtract` 4x` from both sides to eliminate `4x` from the left, but to preserve the equation)

`y = 6 - 4x` (reduce duplicate terms form the left side)

`y = -4x + 6` (re-arrange the terms)

Hence, evaluating the gradient and y intercept of the function `y + 4x = 6` yields `m = -4` (gradient), `b = 6` (y intercept).

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