Step by step
The question
Question: graph y ≤ −2x − 3.
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: y = −2x − 3.
The sign has "or equal to".
So points on the line are answers too.
We draw it solid, like the filled circle on a number line.
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.
b = −3.
Start on the y-axis at −3.
m = −2.
As a fraction: −2/1.
Go right 1,
then down 2.
Dot.
Join the dots: solid.
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 or equal to −3?
No, that is false.
So (0, 0) is not an answer.
3 Shade
So we shade the other side, away from (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.