Mike Hagedorn
CEP 811 STaIR
STANDARDS AND OBJECTIVES
Standards
•
A3.1.1 Write the symbolic forms
of linear functions (standard,
point-slope, and slopeintercept) given appropriate
information, and convert
between forms.
•
A3.1.2 Graph lines (including
those of the form x = h and y =
k) given appropriate
information.
•
A3.1.3 Relate the coefficients
in a linear function to the slope
and x- and y-intercepts of its
graph.
Objectives
•
The learner will review the
three different methods of
graphing linear equations.
•
The learner will be given
specific equations and/or story
problems and will be forced to
decide with method is the most
efficient
INTRODUCTION
This project is designed to allow students to review graphing linear equations on their
own. Use this project as a way to prepare yourself for the test. Take your time
and make sure you are fully comfortable with the content. There will be links
throughout this project that will take you to various web pages and help clarify any
misunderstandings.
DIRECTIONS
Go through each this project by clicking the arrows
Go through and review each method. If you need to review something, you may click
the back button.
Once you have completed the review, complete the practice quiz and attempt to
answer them correctly
If you feel you need to review some more, click the home
button. There will also be various links throughout to help you
which will be underlined in red for you to click on if needed
Move on to the next section
VOCABULARY TO KNOW
•
Ordered pair
•
Linear equation
•
X-intercept
•
Y-intercept
•
Slope
•
Slope intercept form
GRAPH LINEAR EQUATIONS USING TABLES
•
Start with equation in two variables
• Example: 2𝑥 + 5𝑦 = 8
•
A solution is the ordered pair (𝑥, 𝑦)
that produces a true statement
•
Need several (𝑥, 𝑦) to be able to
create a graph
•
Let’s graph −𝟐𝒙 + 𝒚 = −𝟑
• First: make a table by choosing a few values
for x
• Second: substitute each x into the equation
and find the value of y
• Plot the corresponding points on a graph
• Connect the points
x
-2
-1
0
1
2
Y
-7
-5
-3
-1
1
LET’S PRACTICE
Graph the following equation using
a table
3𝑥 + 𝑦 = −2
1. Let’s use −2, −1, 0, 1, 2 for our
x values in our table to find the
corresponding y values
The table as follows
x
−2
−1
0
y
4
1
−2
1
2
−5 −8
2. Now let’s plot the points and
connect the dots
GRAPH LINEAR EQUATIONS USING INTERCEPTS
Intercepts: the two points where the graph of the line crosses the axes
x-intercept: where the graph crosses the x-axis. Will have the ordered pair 𝒙, 𝟎
y-intercept: where the graph crosses the y-axis. Will have the ordered pair 𝟎, 𝒚
To find x-intercept:
Let y = 0,
then solve for x
To find each intercept
To find y-intercept:
Let x = 0,
then solve for y
Once you have the two intercepts, plot them on a graph and connect the dots!
There’s the graph for that equation.
EXAMPLE SOLVING AND GRAPHING INTEREPTS
Find the intercepts of 2𝑥 + 7𝑦 = 28
x-int: Let y = 0
2𝑥 + 7 0 = 14
2𝑥 = 14
2𝑥 14
=
2
2
𝑥=7
y-int: Let x = 0
2(0) + 7𝑦 = 14
7𝑦 = 14
7𝑦 14
=
7
7
𝑦=2
So our 𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 is 7, (7, 0) and our 𝑦 −
𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 is 2 (0, 2)
Now lets graph this!
LET’S PRACTICE
Graph the following linear equation by finding
the intercepts
2𝑥 + 3𝑦 = 12
1.
Find the x-intercept (let y = 0)
2𝑥 + 3(0) = 12
2𝑥 = 12
𝑥=6
(6, 0)
2.
Find the y-intercept (let x = 0)
2 0 + 3𝑦 = 12
3𝑦 = 12
𝑦=4
(0, 4)
3.
Now plot the points (intercepts) on the
graph
GRAPH LINEAR EQUATIONS USING SLOPEINTERCEPT FORM
Easiest way to graph!!!!!!
The equation is: 𝒚 = 𝒎𝒙 + 𝒃; 𝐰𝐡𝐞𝐫𝐞 𝒎 𝐢𝐬 𝐭𝐡𝐞 𝒔𝒍𝒐𝒑𝒆 𝐚𝐧𝐝 𝒃 𝐢𝐬 𝐭𝐡𝐞 𝒚 − 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕
Need to know the slope.
• Can do this by counting the grid lines on a graph if graph is already there, OR
• Using the equation 𝑚 =
𝑦2 −𝑦1
𝑥2 −𝑥1
if two points are known that lie on the line.
• Will commonly be the coefficient or in other words, the number next to the x in
most problems.
The other thing you need is the y-intercept
• Is the constant term in the equation.
Example
𝑦 = 𝒎𝑥 + 𝒃
Slope
y-intecept
𝑦=
𝟏
𝑥+𝟏
𝟑
TO GRAPH USING SLOPE-INTERCEPT FORM
First:
• Get the equation into slopeintercept form (y by itself)
Second:
• Plot the y-intercept on the graph
Third
•
From the y-intercept, apply the
𝑟𝑖𝑠𝑒
slope
to get a second point,
𝑟𝑢𝑛
then connect the dots
2
Example: Graph 𝑦 = 𝑥 + 2;
3
follow the three steps
1. Already in slope-intercept form
2. Plot the y-intercept: b = 2
3. From y-intercept, apply slope
Rise
Run
LET’S PRACTICE
Graph the following equation using slopeintercept form
2𝑥 + 3𝑦 = 6
1. Get equation into slope-intercept form
(get y by itself)
2𝑥 + 3𝑦 = 6
3𝑦 = −2𝑥 + 6
2
𝑦=− 𝑥+2
3
2. Plot y-intercept
𝒓𝒊𝒔𝒆
3. Apply the slope
from the y-intercept
𝒓𝒖𝒏
to get a second point
PRACTICE QUIZ!!!!!!
Choose the correct letter for each question
Be sure took look closely at all information before selecting a choice
Take your time. Use pencil and paper if you need to
PROBLEM #1
Which table matches the following
graph
a)
x
y
−4 −2
8
6
0
2
4
4
2
0
0
2
4
b)
x
−4 −2
y
−10 −7 −4 −1
2
x
−4 −2
0
2
4
y
10
4
1
−2
0
2
4
3
0
−3
c)
7
d)
x
y
−4 −2
9
6
PROBLEM #2
What is the xintercept and yintercept of the
following
equation?
8𝑥 − 5𝑦 = 80
a)
x-intercept: 10 (10, 0)
y-intercept: -16 (0, -16)
b)
x-intercept: -10 (-10, 0)
y-intercept: 16 (0, 16)
c)
x-intercept: 8 (8, 0)
y-intercept: -5 (0, -5)
d)
x-intercept: -8 (-8, 0)
y-intercept: 5 (0, 5)
PROBLEM #3
Which graph matches the following x and y intercepts
𝒙 − 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕: −𝟐 𝒚 − 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕: 𝟒
a)
c)
b)
d)
PROBLEM #4
The slope and y-intercept of the following
graph are?
a)
b)
c)
d)
Slope (m):
4
y-intercept (b):
-7
Slope (m):
-4
y-intercept (b):
-7
Slope (m):
4
y-intercept (b):
7
Slope (m):
-4
y-intercept (b):
7
PROBLEM #5
𝟑
𝟒
Which graph matches the following linear equation? 𝒚 = 𝒙 − 𝟔
a)
c)
b)
d)
TRY AGAIN…
Be sure to check
your math and
watch your signs.
TRY AGAIN…
Put in zero for one
variable, then
solve for the
other
Here is a video to help solve
for the x and y intercept
TRY AGAIN…
Look closely at the
signs of the
values and match
them on the
graph
TRY AGAIN…
Try counting the
grid lines to help.
TRY AGAIN…
Remember our
steps to graph
using slopeintercept form
Start with ?????,
then apply????
GREAT JOB!!!!
GREAT JOB!!!!
GREAT JOB!!!!
GREAT JOB!!!!
GREAT JOB!!!!
Push for the next problem
CONGRATULATIONS!!!!
You completed the tutorial and now are ready for the test.
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