Step by step
The question
Question: graph 3x − 2y < 6 and y < 1.
We shade the answer of each one.
Where both are shaded, both are true.
1 Crossing points of ①
On the x-axis, y = 0.
Put 0 in place of y.
2 times 0 is 0.
Taking away 0 changes nothing.
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3 divided by 3 is 1.
So just x is left.
6 divided by 3 is 2.
So x = 2.
On the y-axis, x = 0.
Put 0 in place of x.
3 times 0 is 0.
0 minus 2y is −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.
Plus over minus is minus.
6 divided by −2 is −3.
So y = −3.
So line ① crosses the axes at (2, 0) and (0, −3).
2 Graph ①
Draw the grid.
①: The sign is less than, with no "or equal to".
So the line is dashed.
Put the two crossing points on the grid,
and join them: dashed.
Which side?
We test one point: (0, 0).
Put x = 0 and y = 0 into ①.
Is 0 less than 6?
Yes, true.
Careful!
The sign alone does not say above or below.
When y has a minus in front, it can turn.
The test point tells us.
So we shade the side with (0, 0), in red.
3 Graph ②
②: The sign is less than, with no "or equal to".
So the line is dashed.
b = 1.
Start on the y-axis at 1.
A flat line through the dot: dashed.
Which side?
We test one point: (0, 0).
Put x = 0 and y = 0 into ②.
Is 0 less than 1?
Yes, true.
So we shade the side with (0, 0), in blue.
4 Where both are shaded
This part is shaded twice.
It is the answer.
5 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: crossing points of ①.
Then: graph ①.
Then: graph ②.
Then: where both are shaded.
Last: check.