Download Linear Equation Packet 1

Name:
Date:
SBCA – MATH 8
Introduction to Graphing Linear Equations
Vocabulary:
• X-Axis:The______________________________________numberlineinthe__________________
plane.
• Y-Axis:The______________________________________numberlineinthe__________________
plane.
• IndependentVariable:Typicallythe_____-value;avariablewhosevaluedoesnot______________
onanothernumber.
• DependentVariable:Typicallythe_____-value;avariablewhosevalue_________________onthe
numberchosenasthe_________________________________________.
• OrderedPair:Apairofnumbersusedto__________________________a_________________on
the_____________________________________________.Thefirstnumber(the_____-value)tells
howfartomove________________________________andthesecondnumber(the______-value)
tellshowfartomove________________________________.
• Origin____________:Thepointwherethe______________________________andthe
_______________________inthe__________________________________________________
intersect(meet).
• CoordinatePlane:The_____________________determinedbythe______________________and
the_____________________________,intersectingatapointcalledthe_____________________.
Eachpointinthecoordinateplanecanbespecifiedbyan________________________
__________________.
• Line:A____________________pathinaplanethatgoeson________________________in
_____________________________directions.
• Slope:Ameasureofthe_____________________________ofaline,ora
_______________________ofaline,connectingtwo_____________________.Itisalsoknownas
a_______________________________________________.
• X-intercept:Wherethegraphofanequationintersects(___________________)the
______________.
• Y-intercept:Wherethegraphofanequationintersects(___________________)the
______________.
• LinearEquation:Anequationthatmakesa_____________________________________whenitis
graphed.Often,itiswrittenintheform_________________________________.
• Therearethreewaystowritealinearequation:
Standard Form
Y-intercept Form
Point-Slope Form
• A,B,andCare________________
• misthe_______________
• (𝑥! , 𝑦! ) and (𝑥! , 𝑦! ) are any
two _____________________
• Startwith
• bisthe
____-_______________________
form,thenuseyourliteralequation
_____-______________________
skillstoputtheequationinto
standardform.
• Useanypointonthegraphtofind
anymissingpartoftheequation
usingyourtwo-stepequation
solvingskills
__________________ on the
line
• misthe__________________
Label the x-axis and the y-axis. Label the origin.
x-intercept:
y-intercept:
Is this line increasing or decreasing?
Write three coordinate points that lie on the line:
Label the x-axis and the y-axis. Label the origin.
x-intercept:
y-intercept:
Is this line increasing or decreasing?
Write three coordinate points that lie on the line:
Using a table to help you graph an equation:
Graph:
𝑦 =𝑥+1
𝑥
𝑥+1
𝑦
Graph: 𝑦 = 2𝑥 − 1
𝑥
𝑦
Graph: 𝑦 = −𝑥 + 3
𝑥
𝑦
Proportional Relationships:
A math relationship describes the relations between the _______________ and the _______________
of ordered pairs.
The set of x-values is called the _____________________.
The set of y-values is called the _____________________.
A relation is proportional if there is a ____________________________________________________.
You can tell if a relation is proportional if its graph goes through the ____________________________.
Proportional equations have the form ___________________________.
What is slope?
The slope of a line measures how ________________________ the line is.
To find the slope of a line, we need to find the relationship between the __________________ and
___________________ of coordinate points on a line.
We use the variable _______ to represent the slope of a line.
Finding the slope of a line:
m =
!"#$
!"#
∆!
(!! !!! )
= ∆! = (!
! !!! )
where (𝑥! , 𝑦! ) and (𝑥! , 𝑦! ) are any two coordinate points on the line.
Using a table to find the slope:
1.
x
y
-2
3
-1
5
0
7
1
9
2
11
m=
Sketch of graph:
2.
m=
x
y
-3
5
-2
2
-1
-1
0
-4
1
-7
Sketch of graph:
3.
x
y
1
-17
2
-13
3
-9
4
-5
5
-1
m=
Sketch of graph:
4.
m=
x
y
-1
1
1
2
3
3
5
4
7
5
Sketch of graph:
Using the slope to describe the graph of the line:
There are ____________________ ways to describe the graph of the line based off of its slope.
1. If the slope is _____________________, then the graph of the line is ________________________.
2. If the slope is _____________________, then the graph of the line is ________________________.
3. If the slope is _____________________, then the graph of the line is ________________________.
4. If the slope is _____________________, then the graph of the line is ________________________.
We can use slope dude to help us remember these descriptions.
∆𝑦
∆𝑥
When slope dude is
skateboarding across the
road, he is having
_________________
_________________
When slope dude is
skateboarding up a hill,
he goes
When slope dude is
skateboarding down a
hill, he says
“_________________,
“_________________,
_________________,
_________________,
_________________.”
_________________.”
When slope dude
skateboards off a cliff,
he is now
____________________
Using a graph to find the slope:
m=
m=
Description of slope:
Description of slope:
m=
m=
Description of slope:
Description of slope:
m=
m=
Description of slope:
Description of slope:
Using two given points:
1. Find the slope of the line that passes through the points (-2, -1) and (4, 3).
2. A line goes through the points (0, 4) and (2, 1). What is the slope of this line?
3. Pablo is 30 feet below the surface of the water 10 seconds after he entered the water. He is 100 feet
below the surface after 40 seconds. What is Pablo’s rate of change?
4. Mia started a savings account with $300. After 4 weeks, she had $350. After 9 weeks, she had $400.
What is the rate of change in money in her savings account per week?
Slope concepts: choose Positive, Negative, Zero, or Undefined.
1. When the dependent variable increases as the independent variable increases,
the rate of change is _______________________________.
2. When the dependent variable stays the same as the independent variable increases,
the rate of change is _______________________________.
3. When the dependent variable decreases as the independent variable increases,
the rate of change is _______________________________.
4. When the dependent variable increase as the independent variable stays the same,
the rate of change is _______________________________.
5. When the dependent variable decreases as the independent variable increases,
the rate of change is _______________________________.
6. When the dependent variable decreases as the independent variable decreases,
the rate of change is _______________________________.
7.Thevariable_____isnot_________________________________sinceit__________________on
thenumberchosenfor______.