Question

How do you write `y - 7 = 4(x + 4)` in standard form?

Answer 1

`4x-y=-23`

Explanation:

`y-7=4(x+4)`

This is in the format of `y-y_1= m(x-x_1)` which is known as the point-slope form. To change this to standard form (`Ax+By=C`), you need to find the values of the points `(x_1,y_1)` and the slope (`m`):

`y-7=4(x+4)`
`y-y_1= m(x-x_1)`

Therefore,

`(x_1,y_1) = (-4, 7)` and `m=4`

`y-7=4(x+4)`

Now simplify and rearrange to get `x` and `y` terms on one side and constants on the other side of equal sign:

`y-7=4(x+4)`
`y-7=4x+16`
`y=4x+16+7`
`y=4x+23`
`-4x+y=23`

This is almost in the format of `Ax+By=C` but `Ax` cannot have a negative sign in front of it. To get rid of this negative, divide both sides of the equation by `-1`:

`(-4x+y)/-1=23/-1`
`4x-y=-23`

Now the equation is in standard form because `A=4`, `B=-1` and `C=-23`.