determine whether the point (-4,3) lies on the graph of x-2y=11
The first coordinate -4 is the value for x.
The second coordinate 3 is the value for y.
[The coordinates are in alphabetical order, x first and y second.
That's a very important thing to know.]
Substitute (-4) for x and (3) for y in the equation and simplify.
If it comes out a true statement, then (-4,3) is a solution, and
it represents a point on the line. If it turns out false, it is
not a solution, and does not represent a point on the line:
x-2y = 11
(-4)-2(3)=11
-4-6=11
-10=11
That's clearly false, so (-4,3) does not lie on the graph of x-2y = 11.
Here is a graph of the line x-2y=11 and the point (-4,3)
[Notice that there was a reason they gave you the point (-4,3).
The reason they gave you that is because the point (3,-4) IS on
the line, and students who get x and y backwards would think it
was on the line, and get the problem wrong.
Look what happens when you substitute x=3, and y=-4 instead:
x-2y = 11
(3)-2(-4) = 11
3+8 = 11
11 = 11
That is true, so the point (3,-4) IS on the line as you can see below:
But the point (-4,3) in NOT on the line.
Edwin
