Question

What is the slope of `3x−6y=12`?

Answer 1

`y=1/2x-2`

Rate of change is `+1/2`

Explanation:

First of all the rate of change is known as the slope of a line in Algebra.

The slope helps determine in which way the line curves/moves. In order to solve for the y we must move the x to the other side of the equation (isolate the variable).

After we have done that we can now begin solving the equation. Since we are solving for y we can't have any numbers with it. So the next step is to divide both sides by -6. In which we end up with:

`color(white)("dddddddddddddddd")y=1/2x-2`.
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Given: `3x-6y=12`

Subtract `3x` from both sides

`3x-6y=12`
`ul(3xcolor(white)("dddddddddd")3xlarr" Subtract")`
`color(white)("d")0-6y=12-3x`

`-6y=-3x+12`

multiply both sides by `color(red)(1/6)`

`color(green)(-6/(color(red)(6))y=-3/(color(red)(6)) x+12/(color(red)(6))`

`-y=-1/2x+6`

Multiply both side by (-1)

`y=1/2x-2`
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The rate of change is the coefficient of `x->1/2`