To answer this I would just sub in the x and y values right? I got a) as my answer since it equals 0.
Which of the following would describe the sketch of the expression xy+2y-3x-6=0
a) the planes x=-2 and y=3
b) the planes x=3 and y=-2
c) the planes x=6 and y=2
d) the planes x=3 and y=6
Actually, the expression is the expanded form of
(x+2)(y-3)=0
which by the zero-product property means
x+2=0 => x=-2, or
y-3=0 => y=3, or
both of the above.
So yes, (a) is correct.
To determine the sketch of the expression xy+2y-3x-6=0, we can rearrange the equation to isolate y:
xy + 2y = 3x + 6
y(x + 2) = 3(x + 2)
Now, let's factor out the common factor (x + 2) from both sides of the equation:
y(x + 2) = 3(x + 2)
Dividing both sides of the equation by (x + 2), we get:
y = 3
Now we have the equation y = 3. This equation represents a horizontal line at y = 3, which means that for any value of x, y will always be 3.
Therefore, the correct answer is:
a) the planes x = -2 and y = 3