Step by step
The question
Question: graph y ≤ −(1/2)x + 2 and y > x − 3.
We shade the answer of each one.
Where both are shaded, both are true.
1 Graph ①
Draw the grid.
①: The sign has "or equal to".
So the line is solid.
b = 2.
Start on the y-axis at 2.
m = −1/2.
Go right 2,
then down 1.
Dot.
Join the dots: solid.
Which side?
We test one point: (0, 0).
Put x = 0 and y = 0 into ①.
Is 0 less than or equal to 2?
Yes, true.
So we shade the side with (0, 0), in red.
2 Graph ②
②: The sign is more than, with no "or equal to".
So the line is dashed.
b = −3.
Start on the y-axis at −3.
m = 1.
Go right 1,
then up 1.
Dot.
Join the dots: dashed.
Which side?
We test one point: (0, 0).
Put x = 0 and y = 0 into ②.
Is 0 more than −3?
Yes, true.
So we shade the side with (0, 0), in blue.
3 Where both are shaded
This part is shaded twice.
It is the answer.
Careful!
The answer is not everything we shaded.
Only the part shaded twice works in both.
4 Check
Let's check with a point in the purple part: (−1, −1).
Put it into ①.
Now ②.
True in both!
So the answer is right.
Let's look back.
First: graph ①.
Then: graph ②.
Then: where both are shaded.
Last: check.