Question

Convert each equation to standard form y-5=-3(x+2)​

Answer 1

3x+y=-1

Explanation:

Standard form is ax+by=c.

So we need to get the x-term and the y-term on the same side together.

First step: Distribute:

y-5=-3x-6

Second step: Add 5 on both sides:

y=-3x-6+5

Third step: Simplify:

y=-3x-1

Fourth step: Add 3x on both sides:

3x+y=-1

We are done because this is in ax+by=c form where a=3,b=1, and c=-1.

The form we started with in this problem is point-slope form:
`y-y1=m(x-x1)`.

So if you follow those steps above for point-slope form you should get your standard form.

Let's do this for the general case.

First step: Distribute:

`y-y_1=mx-mx_1`

Second step: Add
`y_1` on both sides:

`y=mx-mx_1+y_1`

Third step: Simplify:

`y=mx+(-mx_1+y_1)`

Fourth step: Add -mx on both sides:

`y+-mx=-mx_1+y_1`

Answer 2

You said each equation but only posted one.

The standard form takes the place of

Ax + By = C.

y-5 = -3(x+2)​

y - 5 = -3x - 6

y = -3x - 6 + 5

3x + y = -1

Done.