Here is a line.
Here is a line.
The line
crosses
(intersects)
the x-axis
once and the
y-axis once.
•
•
Here is a line.
The two
marked
points are
called the
x-intercept
and the
y-intercept.
•
•
Here is a line.
For this line
the
x-intercept is
(6, 0) or 6,
and the
y-intercept is
(0, -4) or -4.
•
•
Here is a line.
Intercepts
don't have to
be integers.
For this line
the x-intercept
is between 5
and 6 while
the y-intercept
is between 3
and 4.
Here is a line.
This vertical
line has an
x-intercept of
-3. It does not
have an
y-intercept.
Here is a line.
This
horizontal line
has a
y-intercept of
8. It does not
have an xintercept.
Finding intercepts sometimes can
help graph an equation quickly.
Finding intercepts sometimes can
help graph an equation quickly.
2x + 3y = 12
Finding intercepts sometimes can
help graph an equation quickly.
2x + 3y = 12
We can do some mental arithmetic
to determine that if x = 0, then
y = 4, and if y = 0, then x = 6.
2x + 3y = 12
The two
intercepts for
this equation
are:
(0, 4) and (6, 0)
•
•
2x + 3y = 12
The two
intercepts for
this equation
are:
(0, 4) and (6, 0)
The intercepts
allowed us to
graph the line
for this
equation.
•
•
2x + 3y = 12
The two
intercepts for
this equation
are:
(0, 4) and (6, 0)
We can find the
slope of this
line.
•
6 left
4 up
•
2x + 3y = 12
The two
intercepts for
this equation
are:
(0, 4) and (6, 0)
Slope is:
-2
3
•
6 left
4 up
•
6x – 2y = 12
6x – 2y = 12
Let x = 0.
6x – 2y = 12
Let x = 0.
Then,
6 • 0 – 2y = 12
6x – 2y = 12
Let x = 0.
Then,
6 • 0 – 2y = 12
0 – 2y = 12
6x – 2y = 12
Let x = 0.
Then,
6 • 0 – 2y = 12
0 – 2y = 12
-2y = 12
6x – 2y = 12
Let x = 0.
Then,
6 • 0 – 2y = 12
0 – 2y = 12
-2y = 12
y = -6
6x – 2y = 12
Let x = 0.
Then,
6 • 0 – 2y = 12
0 – 2y = 12
-2y = 12
y = -6
The y-intercept is -6 or (0, -6)
6x – 2y = 12
Let y = 0.
6x – 2y = 12
Let y = 0.
Then,
6x – 2 • 0 = 12
6x – 2y = 12
Let y = 0.
Then,
6x – 2 • 0 = 12
6x – 0 = 12
6x – 2y = 12
Let y = 0.
Then,
6x – 2 • 0 = 12
6x – 0 = 12
6x = 12
6x – 2y = 12
Let y = 0.
Then,
6x – 2 • 0 = 12
6x – 0 = 12
6x = 12
x=2
6x – 2y = 12
Let y = 0.
Then,
6x – 2 • 0 = 12
6x – 0 = 12
6x = 12
x=2
The x-intercept is 2 or (2, 0)
6x – 2y = 12
The two
intercepts for
this equation
are:
(0, -6)
and (2, 0)
The intercepts
allowed us to
graph the line
for this
equation.
•
•
6x – 2y = 12
The two
intercepts for
this equation
are:
(0, -6)
and (2, 0)
The intercepts
allowed us to
graph the line
for this
equation.
•
•
6x – 2y = 12
The two
intercepts for
this equation
are:
(0, -6)
and (2, 0)
We can find the
slope of this
line.
6 right
•
2 up
•
6x – 2y = 12
The two
intercepts for
this equation
are:
(0, -6)
and (2, 0)
Slope is
1
3
6 right
•
2 up
•
5x + 7y = 24
5x + 7y = 24
5 • 0 + 7y = 24
5x + 7y = 24
5 • 0 + 7y = 24
7y = 24
5x + 7y = 24
5 • 0 + 7y = 24
7y = 24
y=
24
7
5x + 7y = 24
5x + 7y = 24
5x + 7 • 0 = 24
5x + 7y = 24
5x + 7 • 0 = 24
5x = 24
5x + 7y = 24
5x + 7 • 0 = 24
5x = 24
x=
24
5
5x + 7y = 24
The two
intercepts for
this equation
are:
(0, 24 )
7
and ( 24
, 0)
5
•
•
m=
(0,
24
7
y2 – y1
x2 – x1
) and ( 245 , 0)
m=
(0,
x1
24
7
y2 – y1
x2 – x1
) and ( 245 , 0)
y1
x2 y2
m=
(0,
x1
0–
24
5
24
7
–0
24
7
y2 – y1
x2 – x1
) and ( 245 , 0)
y1
x2 y2
m=
(0,
x1
0–
24
5
24
7
–0
=
24
7
y2 – y1
x2 – x1
) and ( 245 , 0)
y1
- 24
7
24
5
x2 y2
y2 – y1
x2 – x1
m=
(0,
x1
0–
24
5
24
7
–0
=
24
7
) and ( 245 , 0)
x2 y2
y1
- 24
7
24
5
=
- 24 ÷ 24
5
7
y2 – y1
x2 – x1
m=
(0,
x1
0–
24
5
24
7
–0
=
24
7
) and ( 245 , 0)
x2 y2
y1
- 24
7
24
5
=
- 24 ÷ 24
5
7
24 • 5
= 7 24
y2 – y1
x2 – x1
m=
(0,
x1
0–
24
5
24
7
–0
=
24
7
) and ( 245 , 0)
x2 y2
y1
- 24
7
24
5
=
- 24 ÷ 24
5
7
24 • 5
= 7 24
y2 – y1
x2 – x1
m=
(0,
x1
0–
24
5
24
7
–0
=
24
7
) and ( 245 , 0)
x2 y2
y1
- 24
7
24
5
=
- 24 ÷ 24
5
7
5
=
7
-
24 • 5
= 7 24
y2 – y1
x2 – x1
m=
(0,
x1
0–
24
5
24
7
–0
=
24
7
) and ( 245 , 0)
x2 y2
y1
- 24
7
24
5
=
- 24 ÷ 24
5
7
5
=
7
-
24 • 5
= 7 24
5x + 7y = 24
The point where a line crosses the
x-axis is called the x-intercept. The
point where a line crosses the
y-axis is called the y-intercept.
Finding intercepts sometimes can
help graph an equation quickly.