Given linear equation in standard form x-y=-2.
Let us convert it in slope-intercept form first.
x-y =-2.
Subtracting x from both sides
x-x-y = -2-x
-y = -x-2.
Dividing both sides by -1, we get
y= x+2.
We can write it as y=1x+2.
Let us compare it with slope-intercept form y=mx+b.
On comparing, we get slope m= 1 and y-intercept b=2.
Let us check option -3x+3y=6.
Let us check it by converting in slope-intercept form.
Adding 3x on both sides we get
-3x+3x+3y=6+3x
3y = 3x + 6.
Dividing both sides each term by 3.
3y/3 = 3x/3 + 6/3.
y= 1x +2.
On comparing with slope-intercept form y=mx+b.
We got slope m=1 and y-intercept =2.
So, the equation in option B) -3x+3y=6 create a consistent and dependent system with x-y=-2.
