Worked examples
The question
Question: graph x = 3.
x = 3
A new word: vertical.
It means straight up and down.
vertical = up and down
1 Read the equation
x = 3 has no y in it.
So y can be any number.
But x is always 3.
x is always 3
y can be any number
2 Make points
Let's make some points.
Every point has x = 3.
For y, we pick any numbers: −2, 1 and 3.
−2
1
3
3 Plot the points
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 points on the grid: (3, −2),
(3, 1),
and (3, 3).
They stand in a column, right above each other.
4 Draw the line
Join the dots.
The line goes straight up and down.
It is a vertical line.
It never goes across, so we call its slope undefined.
It crosses the x-axis at 3.
So x = 3 is a vertical line.
x = 3 → vertical line
Careful: x = 3 is not a flat line.
It goes up and down.
Careful: x = 3 is not flat!
5 Check
Let's check one more point on the line: (3, 2).
Its x is 3.
So it fits x = 3.
The line is right!
(3, 2): x = 3
Let's look back.
First: read the equation.
Then: make points.
Then: plot the points.
Then: draw the line.
Last: check.
Answer x = 3 → vertical line
▶ Watch it solved
The question
Question: find the vertical line through (2, 5), and graph it.
vertical line through (2, 5)
A new word: vertical.
It means straight up and down.
vertical = up and down
1 Write the equation
A vertical line goes straight up and down.
Every point on it is right above or below (2, 5).
So every point has the same x: 2.
x = 2
So the line is x = 2.
x = 2 has no y in it.
So y can be any number.
But x is always 2.
x is always 2
y can be any number
2 Make points
Let's make some points.
Every point has x = 2.
For y, we pick any numbers: 1, 3 and 5.
1
3
5
3 Plot the points
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 points on the grid: (2, 1),
(2, 3),
and (2, 5).
They stand in a column, right above each other.
4 Draw the line
Join the dots.
The line goes straight up and down.
It is a vertical line.
It never goes across, so we call its slope undefined.
It crosses the x-axis at 2.
So x = 2 is a vertical line.
x = 2 → vertical line
Careful: x = 2 is not a flat line.
It goes up and down.
Careful: x = 2 is not flat!
5 Check
Let's check one more point on the line: (2, 4).
Its x is 2.
So it fits x = 2.
The line is right!
(2, 4): x = 2
Let's look back.
First: write the equation.
Then: make points.
Then: plot the points.
Then: draw the line.
Last: check.
Answer x = 2 → vertical line
▶ Watch it solved
The question
Question: graph x = 3 and y = −2.
x = 3 and y = −2
Two new words.
Vertical means straight up and down.
Horizontal means flat, going across.
vertical = up and down
horizontal = flat
1 Read the equations
x = 3 has only x: x is always 3.
It is a vertical line.
y = −2 has only y: y is always −2.
It is a horizontal line.
x = 3 → vertical
y = −2 → horizontal
2 Draw x = 3
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.
x = 3 crosses the x-axis at 3.
Draw a vertical line through it: straight up and down.
3 Draw y = −2
y = −2 crosses the y-axis at −2.
Draw a horizontal line through it: flat, across.
4 Where they meet
The lines meet at one point.
There x = 3 and y = −2.
So they meet at (3, −2).
(x, y) = (3, −2)
5 Check
Let's check: (3, −2) has x = 3, so it is on the first line.
It has y = −2, so it is on the second line too.
Right!
(3, −2): x = 3, y = −2
Let's look back.
First: read the equations.
Then: draw x = 3.
Then: draw y = −2.
Then: where they meet.
Last: check.
▶ Watch it solved
