Question

How do you write the equation `y+3=3(x+5)` in standard form?

Answer 1

The Standard Form of a Linear Equation is given by

`color(red)(Ax + By = C)`

Hence our Final Solution in Standard Form is

`color(blue)(- 3x+y =12)`

Explanation:

We are given the following equation:

`y + 3 = 3(x + 5)` Equation.1

Using Distributive Property we get,

`y + 3 = 3x + 15`

Add `color(red)((-3))` to both sides to simplify:

`y cancel (+3) + color(red)((cancel(-3))) = 3x + 15 + color(red)((-3))`

On simplification we get,

`y = 3x + 15 + color(red)(-3)`

`rArr y = 3x + 12` ... Equation.2

Note that we now have the equation in Slope-Intercept Form

Using basic algebraic concepts, we can obtain the equation in Standard Form

We want both the `x and y` terms on one side and the constant on the other side of our equation to write in Standard Firm

We will add `color(red)((-3x))` to both sides of our Equation.2 to get

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

`rArr y + color(red)((-3x)) = cancel(3x) + 12 + color(red)(cancel(-3x))`

`rArr y -3x = 12`

Rewriting the equation to match `color(red)(Ax + By = C),` which is the Standard Form we get

`color(blue)( -3x + y = 12)`

Hope this helps.

Answer 2

`3x-y=-12`

Explanation:

`"the equation of a line in "color(blue)"standard form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(Ax+By=C)color(white)(2/2)|)))`

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

`y+3=3x+15`

`"rearrange into standard form"`

`rArr3x-y=-12larrcolor(red)"in standard form"`