1. VOCABULARY Coefficient – (Equation) Value multiplied by a variable
(Table) Rate of Change
(Graph) Slope
ex. Y = 4x The coefficient is
y = 7 - x The coefficient is 4 -1
Constant Term – (Equation) Value NOT multiplied by a variable
(Table) Value of “y” when “x” is zero
(Graph) Y-Intercept
ex. Y = 4x The constant term is
y = 7 - x The constant term is 2 7
Coordinate Pair – (X, Y) Gives the point on a coordinate grid

2. VOCABULARY
Coordinate Pair – (X, Y) Gives the point on a coordinate grid
For example: (5, 3)
Point of Origin – Point where x-axis and y-axis cross
Point of Origin
(0, 0)

3. VOCABULARY Y-Intercept – (Equation) Constant term
(Table) Value of “y” when “x” is zero
(Graph) Point where graphed line
crosses y-axis
Y-Intercept
Point of Intersection – (Graph) Point where 2 (or more) graphed lines cross
(Equation) Shared coordinate pair
will solve both equations
(Table) Common Data
Point of Intersection

4. 4 Ways to Represent a Linear Relationship
INVESTIGATION #1
Independent Variable vs Dependent Variable
(x - axis)
(y - axis)
Ask yourself, “Which variable depends on the other?”
Tips for a Good Graph
Labels
- Title
- Label Independent variable on x-axis (horizontal line)
- Label Dependent variable on y-axis (vertical line)
- Include “units of measure”
- Include a key (if needed)
- Scale: Increments need to be consistent and reasonable
4 Ways to Represent a Linear Relationship
Graph (Straight Line)
Table (Constant Rate of Change)
Equation (Form of y=mx+b)
4) Story Problem / Situation (2 variables – 1 depends on the other)

5. Relating Tables, Graphs, and Equations
INVESTIGATION #2
Relating Tables, Graphs, and Equations
Table: x y
Graph:
- 3
- 2
- 1 1 2 3
- 14
- 10
- 6
- 2 2 6 10 4
Equation: y = 4x - 2 1
Coefficient:
Constant Term: 4
(0, - 2) -2
Slope:
Y - intercept: 4 -2
Rate of Change:
Value of “y” when “x” is zero: 4 -2

6. Symbolic form of a Linear Equation The greater the coefficient-
INVESTIGATION #2 cont.
Symbolic form of a Linear Equation
Y = mx + b
Relationships
The greater the coefficient- Y: m: X: b:
Dependent Variable
-the greater the Rate of Change
-the steeper the slope
(equation)
Coefficient
If the coefficient is positive –
-the “y” values in the table
will increase
-the slope will be positive
(table)
Rate of Change
(graph)
Slope
If the coefficient is negative –
-the “y” values in the table
will decrease
-the slope will be negative
Independent Variable
(equation)
Constant Term
(table)
Value of “y” when “x” is zero
If the constant term is positive –
-the line will cross above the
“point of origin”
(graph)
Y - Intercept
If the constant term is negative –
-the line will cross below the
“point of origin”

7. INVESTIGATION #3 Introduction of the Graphing Calculator
Review “Calculator Tips” & “Trouble Shooting”
( - ) vs. – key
Xmin:
Xmax:
Xscl:
Ymin:
Ymax:
Yscl:
200
-30 50
138
125 10
(10, 125)
Window Settings 78
Xmin:
Xmax:
Xscl:
Ymin:
Ymax:
Yscl: -5
lowest value on the x-axis
-30 50
200 -5 10
highest value on the x-axis 25
Y = 4.7x + 78
number of units each tick mark represents on the x-axis
Y = -1.3x + 138
lowest value on the y-axis
highest value on the y-axis
number of units each tick mark represents on the y-axis

8. Checking with the Equation
INVESTIGATION #3 cont.
Point of Intersection
Y = 4.7x + 78
Y = -1.3x + 138
Using the Table
Using the Graph
Enter both equations in the “y =“ screen
Press “2nd graph” to view the table
Scroll up or down so that “y” values are getting closer together
Search for “Common Data” where the “y” values are the same
Enter both equations in the “y =“ screen
Press “graph” to view the graph
Adjust window settings if needed to view the “Point of Intersection”
Press “2nd Trace” to Calculate
Select # 5 – “Intersect”
Press enter 4 times (until P of I is shown at the base of the screen)
X Y Y2
Common Data
(10,125)
Checking with the Equation
Both equations should solve to be true statements when you substitute the values of the coordinate pair.
Y = 4.7x + 78
125 = 4.7(10) + 78
125 =
125 = 125
Y = -1.3x + 138
125 = -1.3(10) + 138
125 =
125 = 125

9. Parallel and Perpendicular Lines Both lines have a slope of 3
INVESTIGATION #4
Parallel and Perpendicular Lines
Parallel
Perpendicular
Parallel lines will never cross
Perpendicular lines cross at 90 degree angles
Equations with the same coefficient
will have the same slope and
will be parallel
The coefficients of the equations
will be opposite reciprocals
(+ / -)
a/b <-> b/a
Example:
Example:
Y = 3x + 8
Y = 3x + 8
Y = x
Y = /3x
3 and –1/3 are
opposite reciprocals
Slope of 3
Both lines have a slope of 3
Slope of –1/3

10. Eliminate the constant term Eliminate the coefficient
INVESTIGATION #4 cont.
SYMBOLIC METHOD
Each line must contain an equal sign (only one)
Each must contain the variable you are solving for
Y = 4x - 3
Solving for “y”
Solving for “x”
X = 12
y = -11
Y = 4x – 3
Y = 4 (12) – 3
Y = 48 – 3
Y = 45
Y = 4x – 3
-11 = 4x – 3
Eliminate the constant term
+ 3
+ 3
-8 = 4x
Eliminate the coefficient 4 4
-2 = x

11. Calculate Ratio Method
INVESTIGATION #5
SLOPE
Stair Step Method
Calculate Ratio Method
Select 2 points on a graphed line
Connect the points with a “stair step”
Count the number of vertical units (rise)
Count the number of horizontal units (run)
Write the SLOPE as a ratio
Select 2 coordinate pairs from a graphed line
Identify ‘pair 1’ and ‘pair 2’
Use the Slope formula
y1 – y2
x1 – x2
SLOPE =
RISE
RUN 2 1
SLOPE =
(1,- 8) & (5,-16)
x y
Reminder watch for negative slopes!
-16 – (-8)
5 - 1
= - 8 4
= -2 1 2
- 6
Rise is 3, run is 2
Negative slope 3
- 8 2
- 3 2
Slope =
-10
Y = -2x - 6
(0, -2)
Y = -1.5x - 2