Question

I'm having trouble understanding, please help.

Answer 1

2x+y=-4

Explanation:

y-2=-2(x+3) is in point-slope form.

Ax+By=C is standard form.

We have to bring x and y to the same side of the equation.

First, let's distribute.

y-2=-2(x)-2(3)

y-2=-2x-6

Next, we will add 2 to both sides to get rid of the -2 on the left side of the equation.

y=-2x-6+2

Then, we will add 2x to both sides to get rid of the -2x on the right side of the equation.

2x+y=-6+2

Now x and y are on the same side of the equation. We just need to simplify the right side.

2x+y=-4

This is the answer in standard form.

Answer 2

2x + y = -4

Explanation:

`\boxed{\begin{minipage}{5.5 cm}\underline{Standard form of a linear equation}\\\\$Ax+By=C$\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are constants. \\ \phantom{ww}$\bullet$ $A$ must be positive.\\\end{minipage}}`

Given equation:

`y-2=-2(x+3)`

To write the given equation in standard form, collect the terms with variables on the one side of the equation (ensuring the term in x is positive), and collect the constants on the other side of the equation.

Distribute the right side of the equation:

`\implies y-2=-2 \cdot x+(-2) \cdot 3`

`\implies y-2=-2x-6`

Add 2x to both sides of the equation:

`\implies y-2+2x=-2x-6+2x`

`\implies y-2+2x=-6`

Add 2 to both sides of the equation:

`\implies y-2+2x+2=-6+2`

`\implies y+2x=-4`

Rearrange the left side to standard form:

`\implies 2x+y=-4`