Answer:
3x+y=-1
Step-by-step 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: [tex]y-y1=m(x-x1)[/tex].
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:
[tex]y-y_1=mx-mx_1[/tex]
Second step: Add [tex]y_1[/tex] on both sides:
[tex]y=mx-mx_1+y_1[/tex]
Third step: Simplify:
[tex]y=mx+(-mx_1+y_1)[/tex]
Fourth step: Add -mx on both sides:
[tex]y+-mx=-mx_1+y_1[/tex]
