Step by step
The question
Question: graph x + 2y < 4.
The answer is not one point.
It is every point that makes this true.
That is a whole part of the grid.
1 Draw the line
First we draw the line where both sides are equal: x + 2y = 4.
The sign is less than, with no "or equal to".
So points on the line are not answers.
We draw it dashed, like the open circle on a number line.
On the x-axis, y = 0.
Put 0 in place of y.
2 times 0 is 0.
Adding 0 changes nothing.
So x = 4.
On the y-axis, x = 0.
Put 0 in place of x.
0 plus 2y is just 2y.
2y means 2 times y.
We want just y.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just y is left.
4 divided by 2 is 2.
So y = 2.
So the line crosses the axes at (4, 0) and (0, 2).
Draw the grid.
The x-axis goes across.
The y-axis goes up and down.
They meet at 0.
That point is called the origin.
Put the two crossing points on the grid,
and join them: dashed.
2 Test a point
The line cuts the grid in two sides.
One side is the answer.
We test one point: (0, 0).
Zeros are easy to work with.
Put x = 0 and y = 0 in.
Is 0 less than 4?
Yes, that is true.
So (0, 0) is an answer.
3 Shade
So we shade the side with (0, 0).
Every point there is an answer.
4 Check
Let's check with a point in the shaded part: (−2, −1).
Put x = −2 and y = −1 in.
True!
So the shading is right.
Let's look back.
First: draw the line.
Then: test a point.
Then: shade.
Last: check.