Question

How do you write `y-5 = 3/2 (x+4)` in standard form?

Answer 1

`3x-2y=-22`

Explanation:

Standard form for a linear equation is
`color(white)("XXXX")Ax+By=C`
`color(white)("XX")"with "A, B, C in ZZ, A>=0`

Given
`color(white)("XX")y-5=3/2(x+4)`
Multiply both sides by `3` (and simplify the right side)
`color(white)("XX")2y-10=3x+12`
Add 10 to both sides
`color(white)("XX")2y=3x+22`
Subtract `3x` from both sides
`color(white)("XX")-3x+2y=22`
Multiply both sides by `(-1)`
`color(white)("XX")3x-2y=-22`

Answer 2

`3x-2y=-22`=>standard form.

Explanation:

The equation of line in the standard form is:

`Ax + By = C`

where A is a positive integer, and B, and C are integers.

So in this case:

`y - 5 = 3/2(x + 4)` => multiply both sides by 2:

`2y - 10 = 3(x + 4)` => expand the right side:

`2y - 10 = 3x + 12` => rewrite as:

`3x + 12 = 2y - 10`=> subtract 2y from both sides:

`3x-2y+12=-10`=> subtract 12 from both sides:

`3x-2y=-22`=>standard form.