Transcript y-intercept

Algebra 1
November 11, 2013
4.3 Quick Graphs Using Intercepts
Objective
Students will graph a linear equation
using the x and y-intercepts
Before we begin…
• In the previous lesson we graphed a
linear equation by creating a table of
values…
• That is not the only way to graph a
linear equation…
• In this lesson we will look at graphing a
linear equation using the x and yintercepts…that is where the line
crosses the x and y-axes
What does it mean to
INTERCEPT a pass in football?
The path of the defender crosses
the path of the thrown football.
In algebra, what are x- and y-intercepts?
Intercepts
• Intercepts are key points to plot when
graphing an equation. Remember, an
intercepts is a POINT (x,y), and not just a
number!
• Look at the x-axis: What is true of EVERY
point on the axis? (y-value is always 0)
• Look at the y-axis: What is true of EVERY
point on the axis? (x-value is always 0)
X-Intercepts
• The x-intercept is the point at which
the linear equation crosses the x-axis.
• x-intercepts can be written as ordered
pairs and may look like this:
(2,0), (3,0), (-5, 0), (-8, 0)
• Notice that the y-value in the ordered
pair is always zero (0)
Finding the x-intercept
• It’s important to note that the y-value is
always zero because in order to find the
x-intercept you will substitute zero (0) for
y in a linear equation, and solve
algebraically, to find the value of x.
• Let’s look at an example…
Example #1
2x + 3y
=6
2x + 3(0) = 6
2x + 0
To find the x-intercept substitute zero
for y and solve algebraically.
=6
2
2
x
=3
The solution x=3 represents where the
linear equation will cross the x-axis. The
solution can be written as the ordered pair
(3, 0)
Y-Intercepts
• The y-intercept is the point at which a
linear equation crosses the y-axis.
• y-intercepts can be written as ordered
pairs that may look like this:
(0, -2), (0, 4), (0, 2), (0, -1)
• Notice that in the ordered pairs the x-
value is always zero (0)
Finding the y-Intercepts
• It’s important to note that the x-value is
always zero (0) because in order to find
the y-intercept you substitute zero for x
and solve the equation algebraically.
• Let’s continue with example 1 and find
the y-intercept
Example #1 (continued)
2x + 3y
=6
2(0) + 3y = 6
0 + 3y
To find the y-intercept substitute zero
for x and solve algebraically.
=6
3
3
y
=2
The solution y=2 represents where the
linear equation will cross the y-axis. The
solution can be written as the ordered pair
(0, 2)
Example #1 (continued)
• Now that we have found the x and y-
intercepts for the equation 2x + 3y = 6
we can plot the graph of the equation
using the x and y-intercepts
• To plot the graph mark the point at
which the line crosses the x and y-axes
and draw a line between the points
• Let’s see what that looks like…
Example #1 (continued)
y
2x + 3y
=6
x-intercept =3
y-intercept =2
x
(0,2)
(3,0)
Finding intercepts:
• X-intercept: where the function crosses the x-
axis. What is true of every point on the x-axis?
– The y-value is ALWAYS zero.
• Y-intercept: where the function crosses the yaxis. What is true of every point on the y-axis?
– The x-value is ALWAYS zero.
• Can the x-intercept and the y-intercept ever be
the same point?
– YES, if the function crosses through the
origin!
Comments
• Often times students get confused when
working with x and y-intercepts…
• They try to substitute 0 for the intercept
they are looking for….this is incorrect!
– If you are looking for x substitute 0 for y.
– If you are looking for y substitute 0 for x
Practice:
Find the x and y intercepts without
graphing.
1. y – 2x = 9
(-9/2, 0) (0, 9)
2. 6x – 6y = 6
(1, 0) (0, -1)
Comments
• On the next couple of slides are some practice
problems…The answers are on the last slide…
• Do the practice and then check your
answers…If you do not get the same answer
you must question what you did…go back and
problem solve to find the error…
• If you cannot find the error bring your work to
me and I will help…
Your Turn
•
1.
2.
3.
•
4.
5.
6.
Find the x-intercept
x + 3y = 5
3x + 4y = 12
-7x – 3y = 42
Find the y-intercept
y = -2x + 5
y = 7x – 15
3x + 12y = -84
Your Turn
Find the x and y-intercepts, graph the
equation, label the points where the
line crosses the axes.
7. y = x + 2
8. y = -6 + 3x
9. -4x + 3y = 24
10. 2x + 9y = -36
•
Your Turn Solutions
1.
2.
3.
4.
5.
6.
x
x
x
y
y
y
=
=
=
=
=
=
5
4
-6
5
-15
-7
•
7.
8.
9.
10.
Your graph should
have the following as
the x and y-intercepts
x = -2
y=2
x=2
y = -6
x = -6
y=8
x = -18
y = -4
Summary
• A key tool in making learning effective is being
able to summarize what you learned in a lesson in
your own words…
• In this lesson we talked about Quick graphs
using intercepts. Therefore, in your own words
summarize this lesson…be sure to include key
concepts that the lesson covered as well as any
points that are still not clear to you…
• I will give you credit for doing this lesson…please
see the next slide…
Credit
I will add 10 points as an assignment grade for you working
on this lesson…
• To receive the full 10 points you must do the following:
•
– Have your name, date and period as well a lesson number
as a heading.
– Do each of the your turn problems showing all work
– Have a 1 paragraph summary of the lesson in your own
words
•
Please be advised – I will not give any credit for work
submitted:
– Without a complete heading
– Without showing work for the your turn problems
– Without a summary in your own words…